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Jessica Watson

Jessica Watson, the girl who sailed round the world, comes home to cheers

A teenage girl who sailed around the world unaided was greeted by thousands of cheering supporters on her return home to Sydney today after her seven-month voyage.

In her 30ft yacht, Ella's Pink Lady, Jessica Watson, 16, crossed the finish line of her round-the-world journey, which supporters claim makes her the youngest sailor to circle the globe solo, non-stop and unassisted.

"I'm completely overwhelmed. I just don't know what to think and what to say at the moment," Watson said in an interview broadcast live on a screen outside the Sydney Opera House. "It's all a bit much but absolutely amazing."

"She said she'd sail around the world, and she has," her mother, Julie, said as she watched her daughter cruise past the finish line from a nearby boat. "She's home."

The teenager's feat will not be considered an official world record because the World Speed Sailing Record Council discontinued its "youngest" category, which was held by another Australian, Jesse Martin, after he completed the journey in 1999 at the age of 18.

Although Watson sailed nearly 23,000 nautical miles, some sailing enthusiasts have argued that she did not venture far enough north of the equator for her journey to count as a true round-the-world sail as defined by the record council's rules. Watson's managers have dismissed those claims and argued she doesn't need to adhere to the council's rules since they will not be recognising her voyage.

Watson, from Buderim, north of Brisbane, in Queensland, sailed out of Sydney on 18 October amid fierce criticism of her parents for allowing her to attempt such a feat. Throughout her journey they stuck to the view that she was well prepared, noting that she has been sailing since she was eight.

"I don't think any of us would ever doubt Jessica Watson again," said the premier of New South Wales, Kristina Keneally, who greeted her on her return home.

Watson traveled north-east through the South Pacific and across the equator, south to Cape Horn at the tip of South America, across the Atlantic Ocean to South Africa, through the Indian Ocean and around southern Australia.

The route took her through some of the world's most treacherous waters, and she battled through huge storms and suffered seven knockdowns.

But her journey was peppered with moments of beauty. On her blog , she described stunning sunrises over glassy seas, the excitement of spotting a blue whale and the dazzling, eerie sight of a shooting star racing across the night sky above her boat.

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Jessica Nabongo crosses a bridge in Bhutan

She visited every country on Earth. Here’s what she learned.

Jessica Nabongo traveled to all 195 nations and became the first Black woman to have documented this feat.

It all began in Bali. On a two-week vacation there in 2017, Jessica Nabongo was feeling adrift after a career change from corporate desk jockey to entrepreneur. Then she read an article about a traveler who had just visited every country on the planet in record time. Nabongo realized there was a community of people like her—people who long to set foot in all nations. She wanted to become the first Black woman to document doing it.

Nabongo was actually well on her way, since she’d already been to 59 countries. She started traveling at age four, tagging along with her Ugandan parents on family trips from their home in Detroit, Michigan . Little did her parents know what they were setting in motion when they instilled the travel bug in their young daughter.

On October 6, 2019—her late father’s birthday—Nabongo completed her mission when she landed in the Seychelles , having visited 195 countries (193 United Nations member states plus the two non-member states, the Holy See and Palestinian territories). But it’s not just about the country count. Along the way, she became a writer, photographer, and passionate advocate for inclusive and ethical tourism. She shares her adventures on her blog and on Instagram .

Now Nabongo is publishing a book with National Geographic, The Catch Me If You Can ,  which highlights 100 of her favorite countries. Here she talks to us about surprise encounters, banishing fear, and tips for traveling better.

What inspires your adventures?

Curiosity—that’s what’s always inspired me. I have a strong desire to see the differences and similarities in how people live everywhere in the world, even at home in the United States . I put a lot of trust in strangers, and I believe you can travel solo anywhere.

Who was the most interesting person you met?

My guide in Algeria —Zaki. It was toward the end of my journey, and at the time there were a lot of anti-government protests going on there. We were supposed to be touring, but we ended up sitting in a café talking. I’ll never forget what he said: “I’m just living for the sake of living. You can’t have wild ambition around here, especially if you’re the oldest child.” It really struck me. Simply because of where he’d been born, his opportunities were limited to the point where he didn’t even want to think about success.

Do you have any travel heroes?

Barbara Hillary . She was the first Black woman to visit the North and South Poles, and she did it aged 75 and 79—isn’t that wild? The other is Cory Lee . He’s in a wheelchair and has visited 37 countries. I can’t relate to him because I haven’t faced those challenges, but I love that he hasn’t let being in a wheelchair stop him from exploring the world. I also follow Traveling Black Widow on Instagram. She was married for 31 years, but after her partner died, she went on to explore the world. I love her.

When we talk about diversity, people mostly think about racial diversity, but it’s also about abilities, age, and body type. There are so many different types of diversity, and everybody should be seen. I like to see how people are living their lives without boundaries.

( Here’s how travelers of color are smashing stereotypes .)

Before your career as a traveler, you studied international development and worked with the United Nations. Did this help to prepare you?

Learning about political and economic history at the London School of Economics absolutely opened my mind and taught me about the world, and the UN was certainly an interesting experience. My studies gave me an understanding of post-colonial dynamics and how different countries wield their power.

A simple example of how this can apply to travel is the relationship between former colonies and air routes. The easiest way to get to former French colonies, particularly in Africa , would be by flying through Paris —the French airlines there will have a monopoly because of the diaspora.

What was the most extreme place you visited?

Let’s talk about South Sudan . The U.S. Embassy strongly discourages U.S. citizens from traveling there, and I was advised by a diplomat that it was too dangerous. South Sudan is insecure in terms of its government, and, of course, terrible things have happened. But I always say no country in the world is completely safe, and no country in the world is completely unsafe. You find what you’re seeking. What I’m seeking is humanity. I’m seeking love. So I went anyway.

(In this episode of our podcast  Overheard , Jessica Nabongo shares her unique journey to become the first documented Black woman to travel to every country in the world.  Listen now on Apple Podcasts. )

I spent my time there with a South Sudanese woman, Nyankuir. I didn’t want to go to a compound and never leave it. Instead, I visited a cattle camp—cattle are an extremely important aspect of Dinka culture. I spent time speaking to the elders and the children, and I found out my bride price—30 cattle, at most, because at five-foot seven, I’m considered short there.

I also think of my trip to the market. There was an old man sitting right in the middle of it. His face was super wrinkled and I found myself just staring at him. I thought he was begging for money, but it turned out that his children were grown-up and had left home and he didn’t like being home alone. So he sat in the market every day to interact with people. I asked for his picture, and he told me to hold on because he wanted to put his glasses on first. So now I have these two portraits: one of how he wanted to be seen, and one of how I wanted to see him.

Both were beautiful and simple experiences. I never felt afraid. It was a reminder that you should take everything you hear from people with a grain of salt.

What travel kit can’t you do without?

I like mirrorless cameras because they’re lighter—whether they’re Sony or Canon. I think the 24-70mm is the perfect lens, in terms of getting that wide range of shots, from landscape images to beautiful portraits, and being able to move with one lens. Obviously, you can take more than one lens, but if you’re traveling for extended periods you should take a 24-70mm. I also travel with my drone. I have a DJI Mavic Air that I find to be lightweight—and inconspicuous when I need it to be.

Did you ever experience any setbacks?

I don’t believe in failure. And I don’t have the ability to be embarrassed. Embarrassment isn’t a natural human trait, in my eyes—it comes from socialization. If I fell over in the middle of Grand Central Station, I’d laugh at myself. I truly believe that every failure in your life is just an opportunity to learn.

What do you collect while traveling?

Alcohol. In Peru , I got pisco; in Georgia and New Zealand , I bought wine. Waragi—a kind of gin—in Uganda , and more gin in Eritrea . Then rum in Barbados, of course, and rakia in Serbia .

If you could change one thing in the world of travel, what would it be?

Single-use plastic. I wish it didn’t exist. On my travels, I really saw the effects of it. I once went snorkeling in Nauru, one of the world’s least-visited countries, and there was so much rubbish in the water—it broke my heart. I see it all the time, everywhere, but unfortunately mostly in developing countries. Corporations brought in all this plastic and didn’t tell anyone how to dispose of it. These communities are used to organic waste, like banana peel—you throw it out. They have no waste-management system to deal with it.

( We depend on plastic. Now we’re drowning in it .)

What’s the best piece of advice you’ve received?

My mother has always said ‘humble yourself.’ I appreciate it because when you travel, depending on your passport, depending on your social class, depending on so many different things, you can go to places with a lot of ego, or you can humble yourself and know that everyone is equal. It enables you to connect with all types of people, no matter if they’re a man sitting on the floor at the market, or if they’re a general manager at a Four Seasons property. It’s really just about seeing people exactly as they are—human beings. Having humility is so important.

Do you have any advice for someone thinking of embarking on a similar adventure?

Travel with kindness, travel with positive energy and without fear. I think what holds people back a lot of the time is fear of the unknown. What I’ve learned throughout my travels is that most people are good, and because of that, there’s no reason to have an innate fear of a stranger. Most people really want to help you. A lot of the time people are just really happy that you’re in their country.

Has the pandemic caused you to think differently about travel?

I think I’m definitely more conscious about the environment . I always have my reusable water bottle instead of using those little plastic bottles. Even though I find it slightly annoying, it’s something small that I can do. On planes I fly with a reusable cup so that I’m not using plastic cups. The other thing is slowing down. I want to spend more time in places versus always having to get back home. Why do I have to leave? There’s Wi-Fi. I think we’re going to see that trend across the board because everybody’s working remotely.

( Is the office obsolete? Many travelers hope so .)

What are some other things people can do to travel more sustainably?

Single-use plastic is one of the biggest things harming Earth right now, so a lot of my focus is on that. But I also think it’s important to watch how much you waste. If you’re in a restaurant and you don’t have a big appetite, ask for a half portion. It’s about being a deliberate traveler, just taking that extra minute to think how can I have a lower impact on this place that I’m in and on the planet in general.

You took road trips in the U.S. last summer. What did you learn about your home country?

I went to 25 states in 2020. Before I left Michigan, I took a COVID test. Then I drove to New York and started with New England. Then I did Delaware , Maryland . I also road-tripped around Utah and much of the South. Americans live in one of the largest and most diverse countries in the world, but so many people have never been to the national parks in their state or in the neighboring state. And there are all these microcultures, like lobster fishers in Maine . I learned about the Geechee/Gullah culture in South Carolina . I went to Oklahoma and got to learn about the history of Black cowboys. We’re always chasing passport stamps, but how about we explore our own country, whether it’s the U.S., Kenya , or Canada . 

What are some places around the world you’re still longing to visit?

The Okavango Delta in Botswana . I’ve done safaris in almost every African country, but people say that’s one of the best. Also gorilla trekking in Uganda and the beautiful, pristine beaches of Madagasca r. I think I’ll do all three of those this year. My bucket lists don’t last very long.

This article was expanded from one that initially appeared on National Geographic’s U.K. website . The interview has been edited for length and clarity. 

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Mary traveled a highly dangerous path to visit Elizabeth

MARY VISITS ELIZABETH

Fr Lawrence Lew, O.P. | Flickr CC by NC-ND 2.0

St. Luke narrates in his Gospel how the Virgin Mary, after receiving news about her cousin’s remarkable conception in her old age, “arose and went with haste into the hill country, to a city of Judah, and she entered the house of Zechariah and greeted Elizabeth” (Luke 1:39-40).

It is traditionally believed that Mary received the message of Elizabeth’s pregnancy while residing at her home in Nazareth. Elizabeth was living in Ein Karem at the time, and the distance between the two villages is roughly 100 miles.

Ein Karem is on the outskirts of Jerusalem and is about 2,474 feet above sea level, while Nazareth is at 1,138 feet. This means Mary had to trek uphill nearly 1,336 feet in elevation!

Besides the physical toll it must have taken on the newly pregnant Virgin Mary, the path she took had many hidden dangers.

The dirt path that wound through the mountainous region is believed to have been a popular place for bandits, who would surprise unsuspecting travelers.

The good news is that the Virgin Mary was likely not alone. While the Gospel only mentions Mary, it makes sense that Joseph would have ensured the safety of his betrothed.

According to writer J. A. Loarte , “Most likely it was Joseph who arranged the trip, looking for a caravan in which the Blessed Virgin could travel safely. He himself may have accompanied her, at least as far as Jerusalem; some commentators even think he went with Mary right to Ain Karim, which is only five miles from the capital. If so, he would have needed to return immediately to his workshop in Nazareth.”

With this in mind, it’s no surprise that Mary went “in haste” to visit Elizabeth, hoping that their caravan wouldn’t be overrun by those who lurked in the shadows and caves of the mountains.

The Visitation presented many risks to Mary, yet she trusted that God would protect her and allow her to assist her aging cousin. It is a beautiful mystery, one that only deepens when you learn about the geography and the obstacles Mary had to overcome to visit Elizabeth.

NAZARETH,JESUS

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After her North American tour ends, how is Greta Thunberg getting home?

The 60-foot yacht she chartered to get her to New York has returned to Europe, and Thunberg says she does not know how she will return to Sweden

Article content

Greta Thunberg, the 16-year-old Swedish climate activist, has been making waves the world over with powerful speeches and appearances in climate strikes.

Since late August, she’s been on a tour of North America, attending rallies, meeting with world leaders, and speaking at the United Nations Climate Action Summit in New York City. She marched in a climate strike in Edmonton on Friday, Oct. 18.

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Thunberg has said she received many requests to speak at events internationally, but declined due to the extensive travel it would require. But she decided to make an exception to attend the UN climate summit as well as a major UN climate change conference in Santiago, Chile, where her trip is scheduled to end.

I don't know yet how I will get home

Her trip to North America is well-documented — she sailed for 15 days from England to New York on a carbon-neutral racing yacht to avoid the huge impact air travel has on carbon emissions.

But now that she’s finally here, some have begun to wonder: how is she getting back home to Sweden?

Before she left England in August, she said “I don’t know yet how I will get home,” according to the Daily Mail .

For starters, the boat she took to get to New York, the Malizia II, has returned to Europe. Despite trying to avoid carbon emissions, her organization has seen some criticism because the crew returned by plane — her team said the emissions were offset.

  • Swedish activist Greta Thunberg's visit inspires Edmonton climate march

where did she travel

Which means that Thunberg is left with either chartering a plane, which she refuses to do, hopping on a commercial cruise line, which she’s also spoken out against because of the emissions, or chartering another carbon neutral boat to come pick her up.

“Greta doesn’t take airplanes so she’ll have to get to both Chile and back to Sweden using other modes of transportation,” a spokesperson for Thunberg’s team told Vox .

“The details are not confirmed yet.”

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  • climate change

Climate Activist Greta Thunberg, 16, Arrives in New York After Sailing Across the Atlantic

T eenage climate activist Greta Thunberg arrived in New York City on Wednesday after sailing across the Atlantic Ocean to call attention to the need for quick action to save the planet.

Thunberg, a 16-year-old from Sweden, embarked in the racing sailboat Malizia II from Plymouth in the United Kingdom two weeks ago on the trip to the U.S. to attend the United Nations Climate Action Summit, which is scheduled to take place in September at the U.N.’s headquarters in New York.

After disembarking from the vessel at a Manhattan marina, Thunberg was greeted by a crowd of supporters, including a group of fellow high school students carrying homemade signs. The students broke into chants as the sailboat slowly pulled into the marina in Lower Manhattan, including “Sea levels are rising and so are we!” and “There is no Planet B!”

US-ENVIRONMENT-SWEDEN-CLIMATE-THUNBERG

Thunberg seemed a little weary from her journey, but spoke forcefully about climate change. While she doesn’t expect everyone to cross the Atlantic Ocean in a boat like she did, she said that she believes it’s time for people to come together to fight climate change.

“The climate and ecological crisis is a global crisis and the biggest crisis humanity has ever faced,” she said shortly after she stepped on shore. “And if we don’t manage to work together and to cooperate… then we will fail.”

Thunberg said that while she’s hoping to spread the word about climate change, one person isn’t the primary focus of her message––President Donald Trump.

“My message for him is just listen to the science, and he obviously doesn’t do that. As I always say to this question, if no one has been able to convince him about the climate crisis, the urgency, why should I be able to do that?” Thunberg said.

Thunberg launched her campaign for action on climate change just last August, when she sat outside of the Swedish Parliament in Stockholm holding a sign inscribed with the phrase, “Skolstrejk för Klimatet” (School Strike for Climate). In the year since, she helped to organize a March 15 strike believed to have been joined by 1.6 million people in 133 countries; met with world leaders, including Pope Francis; and was nominated for the 2019 Nobel Peace Prize.

Thunberg has drawn attention to the greenhouse gas emissions caused by air travel. In Sweden, she is credited for the spread of “flygskam”––flight shame––which reports say may have encouraged some Swedes to avoid traveling by plane.

Greta Thunberg in New York

The Malizia II is a 60-foot vessel is designed to be emission-free, and is equipped with solar panels, hydro-generators and an onboard lab for measuring CO2 levels and other information about the surface of the ocean.

The teen set sail two weeks ago with a small group, including her father, Svante Thunberg, and co-skippers Pierre Casiraghi––grandson of Rainier III, Prince of Monaco and Grace Kelly––and professional sailor Boris Herrmann, who has travelled around the world three times and made “countless” journeys across the Atlantic, according to Herrmann’s website .

As the vessel was designed for racing, it was built for speed––but not comfort. Herrmann’s website acknowledges that the boat lacks many amenities, including cooking facilities, a toilet and a shower, although “comfortable mattresses” were added for Thunberg’s voyage.

Several young people said that they had first learned about Thunberg from YouTube, but had been motivated to act because they’ve learned how climate change is impacting people around the world.

Olivia Wohlgemuth, a 16-year-old student at LaGuardia High School, tells TIME that while she’s worried about the future, protesting to raise awareness gives her hope.

“I always feel so hopeful at protests. Climate change can be so bleak and action can be an antidote to that,” Wohlgemuth said.

Greta Thunberg in New York

Several teenagers, including 15-year-old Dwight School student Alessandro Dal Bon, said that Thunberg had been the inspiration for them to get involved with climate activism.

“She’s not afraid of anyone. She’s not afraid of the politicians, she’s not afraid of the businessmen. She just wants to get her message out there. And she’s willing to do anything for that. She’s willing to cross the Atlantic Ocean for 15 days on a small boat to do that. That just shows you how determined she is,” Dal Bon says.

Thunberg thanked the sailboat’s team and said that the trip had been “surprisingly good,” noting that she hadn’t gotten seasick. She said that she would miss feeling “disconnected” from the world during the journey.

“To just sit, literally sit for hours, and just stare at the ocean not doing anything. That was great. And I’m going to miss that a lot,” Thunberg said. “And of course, to be in this wilderness, the ocean, and to see the beauty of it. “

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  • 2.6 Solve a Formula for a Specific Variable
  • Introduction
  • 1.1 Introduction to Whole Numbers
  • 1.2 Use the Language of Algebra
  • 1.3 Add and Subtract Integers
  • 1.4 Multiply and Divide Integers
  • 1.5 Visualize Fractions
  • 1.6 Add and Subtract Fractions
  • 1.7 Decimals
  • 1.8 The Real Numbers
  • 1.9 Properties of Real Numbers
  • 1.10 Systems of Measurement
  • Key Concepts
  • Review Exercises
  • Practice Test
  • 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
  • 2.2 Solve Equations using the Division and Multiplication Properties of Equality
  • 2.3 Solve Equations with Variables and Constants on Both Sides
  • 2.4 Use a General Strategy to Solve Linear Equations
  • 2.5 Solve Equations with Fractions or Decimals
  • 2.7 Solve Linear Inequalities
  • 3.1 Use a Problem-Solving Strategy
  • 3.2 Solve Percent Applications
  • 3.3 Solve Mixture Applications
  • 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
  • 3.5 Solve Uniform Motion Applications
  • 3.6 Solve Applications with Linear Inequalities
  • 4.1 Use the Rectangular Coordinate System
  • 4.2 Graph Linear Equations in Two Variables
  • 4.3 Graph with Intercepts
  • 4.4 Understand Slope of a Line
  • 4.5 Use the Slope-Intercept Form of an Equation of a Line
  • 4.6 Find the Equation of a Line
  • 4.7 Graphs of Linear Inequalities
  • 5.1 Solve Systems of Equations by Graphing
  • 5.2 Solving Systems of Equations by Substitution
  • 5.3 Solve Systems of Equations by Elimination
  • 5.4 Solve Applications with Systems of Equations
  • 5.5 Solve Mixture Applications with Systems of Equations
  • 5.6 Graphing Systems of Linear Inequalities
  • 6.1 Add and Subtract Polynomials
  • 6.2 Use Multiplication Properties of Exponents
  • 6.3 Multiply Polynomials
  • 6.4 Special Products
  • 6.5 Divide Monomials
  • 6.6 Divide Polynomials
  • 6.7 Integer Exponents and Scientific Notation
  • 7.1 Greatest Common Factor and Factor by Grouping
  • 7.2 Factor Trinomials of the Form x2+bx+c
  • 7.3 Factor Trinomials of the Form ax2+bx+c
  • 7.4 Factor Special Products
  • 7.5 General Strategy for Factoring Polynomials
  • 7.6 Quadratic Equations
  • 8.1 Simplify Rational Expressions
  • 8.2 Multiply and Divide Rational Expressions
  • 8.3 Add and Subtract Rational Expressions with a Common Denominator
  • 8.4 Add and Subtract Rational Expressions with Unlike Denominators
  • 8.5 Simplify Complex Rational Expressions
  • 8.6 Solve Rational Equations
  • 8.7 Solve Proportion and Similar Figure Applications
  • 8.8 Solve Uniform Motion and Work Applications
  • 8.9 Use Direct and Inverse Variation
  • 9.1 Simplify and Use Square Roots
  • 9.2 Simplify Square Roots
  • 9.3 Add and Subtract Square Roots
  • 9.4 Multiply Square Roots
  • 9.5 Divide Square Roots
  • 9.6 Solve Equations with Square Roots
  • 9.7 Higher Roots
  • 9.8 Rational Exponents
  • 10.1 Solve Quadratic Equations Using the Square Root Property
  • 10.2 Solve Quadratic Equations by Completing the Square
  • 10.3 Solve Quadratic Equations Using the Quadratic Formula
  • 10.4 Solve Applications Modeled by Quadratic Equations
  • 10.5 Graphing Quadratic Equations in Two Variables

Learning Objectives

By the end of this section, you will be able to:

  • Use the Distance, Rate, and Time formula
  • Solve a formula for a specific variable

Be Prepared 2.16

Before you get started, take this readiness quiz.

Solve: 15 t = 120 . 15 t = 120 . If you missed this problem, review Example 2.13 .

Be Prepared 2.17

Solve: 6 x + 24 = 96 . 6 x + 24 = 96 . If you missed this problem, review Example 2.27 .

Use the Distance, Rate, and Time Formula

One formula you will use often in algebra and in everyday life is the formula for distance traveled by an object moving at a constant rate. Rate is an equivalent word for “speed.” The basic idea of rate may already familiar to you. Do you know what distance you travel if you drive at a steady rate of 60 miles per hour for 2 hours? (This might happen if you use your car’s cruise control while driving on the highway.) If you said 120 miles, you already know how to use this formula!

Distance, Rate, and Time

For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula:

We will use the Strategy for Solving Applications that we used earlier in this chapter. When our problem requires a formula, we change Step 4. In place of writing a sentence, we write the appropriate formula. We write the revised steps here for reference.

Solve an application (with a formula).

  • Step 1. Read the problem. Make sure all the words and ideas are understood.
  • Step 2. Identify what we are looking for.
  • Step 3. Name what we are looking for. Choose a variable to represent that quantity.
  • Step 4. Translate into an equation. Write the appropriate formula for the situation. Substitute in the given information.
  • Step 5. Solve the equation using good algebra techniques.
  • Step 6. Check the answer in the problem and make sure it makes sense.
  • Step 7. Answer the question with a complete sentence.

You may want to create a mini-chart to summarize the information in the problem. See the chart in this first example.

Example 2.58

Jamal rides his bike at a uniform rate of 12 miles per hour for 3 1 2 3 1 2 hours. What distance has he traveled?

Try It 2.115

Lindsay drove for 5 1 2 5 1 2 hours at 60 miles per hour. How much distance did she travel?

Try It 2.116

Trinh walked for 2 1 3 2 1 3 hours at 3 miles per hour. How far did she walk?

Example 2.59

Rey is planning to drive from his house in San Diego to visit his grandmother in Sacramento, a distance of 520 miles. If he can drive at a steady rate of 65 miles per hour, how many hours will the trip take?

Try It 2.117

Lee wants to drive from Phoenix to his brother’s apartment in San Francisco, a distance of 770 miles. If he drives at a steady rate of 70 miles per hour, how many hours will the trip take?

Try It 2.118

Yesenia is 168 miles from Chicago. If she needs to be in Chicago in 3 hours, at what rate does she need to drive?

Solve a Formula for a Specific Variable

You are probably familiar with some geometry formulas. A formula is a mathematical description of the relationship between variables. Formulas are also used in the sciences, such as chemistry, physics, and biology. In medicine they are used for calculations for dispensing medicine or determining body mass index. Spreadsheet programs rely on formulas to make calculations. It is important to be familiar with formulas and be able to manipulate them easily.

In Example 2.58 and Example 2.59 , we used the formula d = r t d = r t . This formula gives the value of d d , distance, when you substitute in the values of r and t r and t , the rate and time. But in Example 2.59 , we had to find the value of t t . We substituted in values of d and r d and r and then used algebra to solve for t t . If you had to do this often, you might wonder why there is not a formula that gives the value of t t when you substitute in the values of d and r d and r . We can make a formula like this by solving the formula d = r t d = r t for t t .

To solve a formula for a specific variable means to isolate that variable on one side of the equals sign with a coefficient of 1. All other variables and constants are on the other side of the equals sign. To see how to solve a formula for a specific variable, we will start with the distance, rate and time formula.

Example 2.60

Solve the formula d = r t d = r t for t t :

  • ⓐ when d = 520 d = 520 and r = 65 r = 65
  • ⓑ in general

We will write the solutions side-by-side to demonstrate that solving a formula in general uses the same steps as when we have numbers to substitute.

We say the formula t = d r t = d r is solved for t t .

Try It 2.119

Solve the formula d = r t d = r t for r r :

ⓐ when d = 180 and t = 4 d = 180 and t = 4 ⓑ in general

Try It 2.120

ⓐ when d = 780 and t = 12 d = 780 and t = 12 ⓑ in general

Example 2.61

Solve the formula A = 1 2 b h A = 1 2 b h for h h :

ⓐ when A = 90 A = 90 and b = 15 b = 15 ⓑ in general

We can now find the height of a triangle, if we know the area and the base, by using the formula h = 2 A b h = 2 A b .

Try It 2.121

Use the formula A = 1 2 b h A = 1 2 b h to solve for h h :

ⓐ when A = 170 A = 170 and b = 17 b = 17 ⓑ in general

Try It 2.122

Use the formula A = 1 2 b h A = 1 2 b h to solve for b b :

ⓐ when A = 62 A = 62 and h = 31 h = 31 ⓑ in general

The formula I = P r t I = P r t is used to calculate simple interest, I , for a principal, P , invested at rate, r , for t years.

Example 2.62

Solve the formula I = P r t I = P r t to find the principal, P P :

ⓐ when I = $ 5,600 , r = 4 % , t = 7 years I = $ 5,600 , r = 4 % , t = 7 years ⓑ in general

Try It 2.123

Use the formula I = P r t I = P r t to find the principal, P P :

ⓐ when I = $ 2,160 , r = 6 % , t = 3 years I = $ 2,160 , r = 6 % , t = 3 years ⓑ in general

Try It 2.124

ⓐ when I = $ 5,400 , r = 12 % , t = 5 years I = $ 5,400 , r = 12 % , t = 5 years ⓑ in general

Later in this class, and in future algebra classes, you’ll encounter equations that relate two variables, usually x and y . You might be given an equation that is solved for y and need to solve it for x , or vice versa. In the following example, we’re given an equation with both x and y on the same side and we’ll solve it for y .

Example 2.63

Solve the formula 3 x + 2 y = 18 3 x + 2 y = 18 for y :

ⓐ when x = 4 x = 4 ⓑ in general

Try It 2.125

Solve the formula 3 x + 4 y = 10 3 x + 4 y = 10 for y :

ⓐ when x = 14 3 x = 14 3 ⓑ in general

Try It 2.126

Solve the formula 5 x + 2 y = 18 5 x + 2 y = 18 for y:

In Examples 1.60 through 1.64 we used the numbers in part ⓐ as a guide to solving in general in part ⓑ . Now we will solve a formula in general without using numbers as a guide.

Example 2.64

Solve the formula P = a + b + c P = a + b + c for a a .

Try It 2.127

Solve the formula P = a + b + c P = a + b + c for b .

Try It 2.128

Solve the formula P = a + b + c P = a + b + c for c .

Example 2.65

Solve the formula 6 x + 5 y = 13 6 x + 5 y = 13 for y.

The fraction is simplified. We cannot divide 13 − 6 x 13 − 6 x by 5.

Try It 2.129

Solve the formula 4 x + 7 y = 9 4 x + 7 y = 9 for y.

Try It 2.130

Solve the formula 5 x + 8 y = 1 5 x + 8 y = 1 for y.

Practice Makes Perfect

In the following exercises, solve.

Steve drove for 8 1 2 8 1 2 hours at 72 miles per hour. How much distance did he travel?

Socorro drove for 4 5 6 4 5 6 hours at 60 miles per hour. How much distance did she travel?

Yuki walked for 1 3 4 1 3 4 hours at 4 miles per hour. How far did she walk?

Francie rode her bike for 2 1 2 2 1 2 hours at 12 miles per hour. How far did she ride?

Connor wants to drive from Tucson to the Grand Canyon, a distance of 338 miles. If he drives at a steady rate of 52 miles per hour, how many hours will the trip take?

Megan is taking the bus from New York City to Montreal. The distance is 380 miles and the bus travels at a steady rate of 76 miles per hour. How long will the bus ride be?

Aurelia is driving from Miami to Orlando at a rate of 65 miles per hour. The distance is 235 miles. To the nearest tenth of an hour, how long will the trip take?

Kareem wants to ride his bike from St. Louis to Champaign, Illinois. The distance is 180 miles. If he rides at a steady rate of 16 miles per hour, how many hours will the trip take?

Javier is driving to Bangor, 240 miles away. If he needs to be in Bangor in 4 hours, at what rate does he need to drive?

Alejandra is driving to Cincinnati, 450 miles away. If she wants to be there in 6 hours, at what rate does she need to drive?

Aisha took the train from Spokane to Seattle. The distance is 280 miles and the trip took 3.5 hours. What was the speed of the train?

Philip got a ride with a friend from Denver to Las Vegas, a distance of 750 miles. If the trip took 10 hours, how fast was the friend driving?

In the following exercises, use the formula d = r t d = r t .

Solve for t t ⓐ when d = 350 d = 350 and r = 70 r = 70 ⓑ in general

Solve for t t ⓐ when d = 240 and r = 60 d = 240 and r = 60 ⓑ in general

Solve for t t ⓐ when d = 510 and r = 60 d = 510 and r = 60 ⓑ in general

Solve for t t ⓐ when d = 175 and r = 50 d = 175 and r = 50 ⓑ in general

Solve for r r ⓐ when d = 204 and t = 3 d = 204 and t = 3 ⓑ in general

Solve for r r ⓐ when d = 420 and t = 6 d = 420 and t = 6 ⓑ in general

Solve for r r ⓐ when d = 160 and t = 2.5 d = 160 and t = 2.5 ⓑ in general

Solve for r r ⓐ when d = 180 and t = 4.5 d = 180 and t = 4.5 ⓑ in general

In the following exercises, use the formula A = 1 2 b h A = 1 2 b h .

Solve for b b ⓐ when A = 126 and h = 18 A = 126 and h = 18 ⓑ in general

Solve for h h ⓐ when A = 176 and b = 22 A = 176 and b = 22 ⓑ in general

Solve for h h ⓐ when A = 375 and b = 25 A = 375 and b = 25 ⓑ in general

Solve for b b ⓐ when A = 65 and h = 13 A = 65 and h = 13 ⓑ in general

In the following exercises, use the formula I = Prt .

Solve for the principal, P for ⓐ I = $ 5,480 , r = 4 % , I = $ 5,480 , r = 4 % , t = 7 years t = 7 years ⓑ in general

Solve for the principal, P for ⓐ I = $ 3,950 , r = 6 % , I = $ 3,950 , r = 6 % , t = 5 years t = 5 years ⓑ in general

Solve for the time, t for ⓐ I = $ 2,376 , P = $ 9,000 , I = $ 2,376 , P = $ 9,000 , r = 4.4 % r = 4.4 % ⓑ in general

Solve for the time, t for ⓐ I = $ 624 , P = $ 6,000 , I = $ 624 , P = $ 6,000 , r = 5.2 % r = 5.2 % ⓑ in general

Solve the formula 2 x + 3 y = 12 2 x + 3 y = 12 for y ⓐ when x = 3 x = 3 ⓑ in general

Solve the formula 5 x + 2 y = 10 5 x + 2 y = 10 for y ⓐ when x = 4 x = 4 ⓑ in general

Solve the formula 3 x − y = 7 3 x − y = 7 for y ⓐ when x = −2 x = −2 ⓑ in general

Solve the formula 4 x + y = 5 4 x + y = 5 for y ⓐ when x = −3 x = −3 ⓑ in general

Solve a + b = 90 a + b = 90 for b b .

Solve a + b = 90 a + b = 90 for a a .

Solve 180 = a + b + c 180 = a + b + c for a a .

Solve 180 = a + b + c 180 = a + b + c for c c .

Solve the formula 8 x + y = 15 8 x + y = 15 for y.

Solve the formula 9 x + y = 13 9 x + y = 13 for y.

Solve the formula −4 x + y = −6 −4 x + y = −6 for y.

Solve the formula −5 x + y = −1 −5 x + y = −1 for y.

Solve the formula 4 x + 3 y = 7 4 x + 3 y = 7 for y .

Solve the formula 3 x + 2 y = 11 3 x + 2 y = 11 for y .

Solve the formula x − y = −4 x − y = −4 for y .

Solve the formula x − y = −3 x − y = −3 for y .

Solve the formula P = 2 L + 2 W P = 2 L + 2 W for L L .

Solve the formula P = 2 L + 2 W P = 2 L + 2 W for W W .

Solve the formula C = π d C = π d for d d .

Solve the formula C = π d C = π d for π π .

Solve the formula V = L W H V = L W H for L L .

Solve the formula V = L W H V = L W H for H H .

Everyday Math

Converting temperature While on a tour in Greece, Tatyana saw that the temperature was 40 o Celsius. Solve for F in the formula C = 5 9 ( F − 32 ) C = 5 9 ( F − 32 ) to find the Fahrenheit temperature.

Converting temperature Yon was visiting the United States and he saw that the temperature in Seattle one day was 50 o Fahrenheit. Solve for C in the formula F = 9 5 C + 32 F = 9 5 C + 32 to find the Celsius temperature.

Writing Exercises

Solve the equation 2 x + 3 y = 6 2 x + 3 y = 6 for y y ⓐ when x = −3 x = −3 ⓑ in general ⓒ Which solution is easier for you, ⓐ or ⓑ ? Why?

Solve the equation 5 x − 2 y = 10 5 x − 2 y = 10 for x x ⓐ when y = 10 y = 10 ⓑ in general ⓒ Which solution is easier for you, ⓐ or ⓑ ? Why?

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?

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Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

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  • Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis
  • Publisher/website: OpenStax
  • Book title: Elementary Algebra 2e
  • Publication date: Apr 22, 2020
  • Location: Houston, Texas
  • Book URL: https://openstax.org/books/elementary-algebra-2e/pages/1-introduction
  • Section URL: https://openstax.org/books/elementary-algebra-2e/pages/2-6-solve-a-formula-for-a-specific-variable

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Taylor Swift’s Journey to Las Vegas Ends With Super Bowl Win

The pop singer had to travel across the globe (and through time, in a sense) to make the game. She watched Travis Kelce and Kansas City beat San Francisco in overtime.

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Travis Kelce, in his shoulder pads and a white hat, is hugged by Taylor Swift, who is wearing a black top. They are surrounded by people on the field after a game.

By Benjamin Hoffman

The Kansas City Chiefs won their third Super Bowl title in the last five seasons by beating the San Francisco 49ers in overtime, 25-22, on Sunday. While some N.F.L. players go their entire career without winning a championship, one of Kansas City’s newcomers came away a winner in their 13th game.

Taylor Swift, who has been dating Travis Kelce, Kansas City’s star tight end, changed the N.F.L. conversation all season, attracting a new audience for the league and inspiring strong emotions (both positive and negative) among fans. And, as expected, she was at the stadium and cheering on Mr. Kelce and the Chiefs in their come-from-behind win.

After the game, Ms. Swift celebrated on the field with Donna Kelce and the rest of Kansas City’s friends and family as Mr. Kelce sang a truly memorable rendition of “Viva Las Vegas.”

She then found Mr. Kelce to celebrate after his speech.

“It was unbelievable,” she said to him in a video shot on the field after the game. “It was one of the craziest things I’ve ever experienced.”

Mr. Kelce, who is expected to celebrate with teammates at a victory parade in Kansas City on Wednesday, was asked after the game if any couple had ever had a better week than Ms. Swift winning two Grammys and Mr. Kelce winning the Super Bowl .

“On top of the world right now, baby,” he said. “It’s a good feeling.”

Taylor’s Journey

Was there any doubt she’d go, but wasn’t she in tokyo … the night before, who did she sit with, why did this get so much attention, this is taylor, surely there was some numerology involved, will she make it to the victory parade.

Ms. Swift, as you may have heard, is good at keeping secrets . Her plans, beyond concert dates, are rarely announced in advance. That has led some to devise their own methods for figuring out what she’s up to. Ahead of a Kansas City game in October, for example, an NBC producer said he had a spotter plane searching the area around MetLife Stadium for police escorts in hopes of alerting the television crew if she showed up (she did).

Mr. Kelce was inundated with questions about Ms. Swift last week, and while he said he had heard some of her upcoming album — spoiler: he likes it — he did not offer any details about whether she would be at the game.

But she arrived at Allegiant Stadium on Sunday afternoon in time for the game. She walked the tunnels of the stadium wearing a black top and pants while carrying a red jacket over her shoulder — and wearing a custom diamond and gold necklace by Stephanie Gottlieb with Mr. Kelce’s No. 87 on it — and then headed up to the luxury suites.

The CBS broadcast did not show her much in a quiet first half for Mr. Kelce and Kansas City, but she was shown routinely as the team came back to win the game, with Mr. Kelce providing several key plays in the fourth quarter and overtime.

She sure was. Her Eras Tour resumed recently, and on Saturday night in Tokyo she performed yet another marathon set of her extensive catalog of songs. With flights from Tokyo to Las Vegas often taking 13 hours or more, and human beings requiring sleep, some worried she might not make the game.

The Japanese Embassy in Washington pointed out that timing was not a real hurdle for Ms. Swift. First of all, a private jet shortens the journey (and provides a place to sleep peacefully if needed). Second of all, the international date line was her friend.

In 1873, before the international date line officially existed, the author Jules Verne mapped out Ms. Swift’s time advantage in “Around the World in 80 Days.” In the book, the protagonist Phileas Fogg believes he has lost his bet only to realize the distance and direction of his travels had saved him:

In journeying eastward he had gone towards the sun, and the days therefore diminished for him as many times four minutes as he crossed degrees in this direction. There are three hundred and sixty degrees on the circumference of the earth; and these three hundred and sixty degrees, multiplied by four minutes, gives precisely twenty-four hours — that is, the day unconsciously gained. In other words, while Phileas Fogg, going eastward, saw the sun pass the meridian eighty times, his friends in London only saw it pass the meridian seventy-nine times. This is why they awaited him at the Reform Club on Saturday, and not Sunday, as Mr. Fogg thought.

Or, as “The West Wing” summarized more succinctly in a scene that discussed President Bartlett’s journey from Tokyo to Washington, D.C. (and that recently went viral online):

Josh: He’s gonna land in Washington an hour before he took off? Sam: Yeah.

For older generations, those scenes helped explain the logistics of the international date line. For Gen Z and younger, their frame of reference will likely be … when Taylor Swift flew to Las Vegas for the Super Bowl.

During the regular season, Ms. Swift attended numerous games in Kansas City while seated in a luxury suite controlled by Mr. Kelce’s close friend and longtime teammate, Patrick Mahomes. She appeared to become fast friends with Mr. Mahomes’s wife, Brittany, and was regularly seen with other members of the Mahomes family.

She has also spent time at games with Mr. Kelce’s parents, Donna and Ed, and her own father, mother and brother came with her to a game on Christmas. During Ms. Swift’s trip to New Jersey for a Chiefs-Jets game she was seated with friends like the actors Ryan Reynolds and Blake Lively.

At a playoff game in Buffalo last month, she and Kylie Kelce were among those shown reacting to Jason Kelce’s shirtless bellowing and fraternizing with the crowd.

And at the A.F.C. championship game in Baltimore, she was surrounded by Mr. Kelce’s family and associates, including Donna and Ed Kelce, Jason and Kylie Kelce and Mr. Kelce’s managers , Aaron and André Eanes. There were also a few of Ms. Swift’s friends, like the actress Keleigh Teller and the model Cara Delevingne.

For the Super Bowl, it was a similar crowd, with the Kelces, the Eanes brothers and Ms. Lively there with Ms. Swift and her family. Additions to the typical crew, in terms of who she was shown with during the game, included the rapper Ice Spice — who entered the stadium with Ms. Swift — and the singer Lana Del Rey.

No one ever seemed to mind Jack Nicholson being a fixture at Los Angeles Lakers games, or Spike Lee being more associated with the New York Knicks than most of the team’s players. Drake got only a slap on the wrist when he began walking onto the court during timeouts at Toronto Raptors playoff games. But even though Ms. Swift receives relatively little airtime during the broadcasts of Kansas City’s games, she has become a target for those who still think she’s getting outsize attention.

“The attention is there because the audience wants to see it,” Jason Kelce, brother of Travis, said in an interview during last week’s Pro Bowl festivities. “If people didn’t want to see it they wouldn’t be showing it.”

As Ms. Swift put it , “a few dads, Brads, and Chads” may be angry, but the TV networks are thrilled. A ratings analysis by The Upshot indicated that she very well may be a driving factor for the league’s increased audience. Coach Andy Reid of the Chiefs has repeatedly said that he’s happy to have her around, and the N.F.L., which is enjoying an unexpected expansion of its built-in audience, has fully embraced her association with the league.

“N.F.L. fans come in all types — even global sensations,” said Alex Riethmiller, an N.F.L. spokesman. “We’re glad to have Taylor on board.”

Ms. Swift has said she loves the number 13, and her fans can seemingly find it everywhere. In the case of this year’s Super Bowl, the examples are plentiful:

Super Bowl 58 (5+8=13)

Feb. 11, 2/11 (2+11=13)

Kansas City is playing the 49ers (4+9=13)

The 49ers were the No. 1 seed in the N.F.C., while the Chiefs were the No. 3 seed in the A.F.C. (1 and 3 — 13)

It was unclear going into the day if it was a good or bad sign that San Francisco’s starting quarterback, Brock Purdy, wears No. 13. But in the end that did not matter, as Ms. Swift’s 13th N.F.L. game of the season ended with a Chiefs win.

Kansas City’s mayor, Quinton Lucas, said on X that a victory parade will be held on Wednesday (weather permitting). While there will surely be a great deal of speculation about whether Ms. Swift will attend, her Eras Tour resumes in Melbourne on Friday, so the logistics would be even trickier than her trip to Las Vegas from Tokyo.

Benjamin Hoffman is a senior editor who writes, assigns and edits stories primarily on the intersection between sports, lifestyle and culture. More about Benjamin Hoffman

How eco-warrior Greta Thunberg travels

Climate change activist to sail to US on ‘zero-carbon’ racing yacht to attend key summits

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Swedish climate change activist Greta Thunberg has found a suitably green way to travel from the UK to the US in order to spread her message - a high-speed racing yacht.

The 16-year-old is taking a sabbatical year from school to focus on her campaigning, but had been puzzling over how to cross the Atlantic to attend two key United Nations climate summits after travelling to Britain by train in April, reports The Times . Thunberg has described the summits - on 23 September in New York and 2-13 December in Santiago, Chile - as “pretty much where our future will be decided”, adds The Guardian .

“It’s on the other side of the Atlantic Ocean,” she said in June. “And there are no trains going there. And since I don’t fly, because of the enormous climate impact of aviation, it’s going to be a challenge.”

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The Stockholm-based teenager, who inspired the Fridays for Future global school climate strike movement, told the Associated Press (AP) that she did not want to travel by cruise ship either, because of their high emissions.

“Taking a boat to North America is basically impossible,” she said. “I have had countless people helping me, trying to contact different boats.”

However, yesterday Thunberg announced on Twitter yesterday that she had accepted “a ride on the 60ft racing boat Malizia II” and will set sail to New York City in mid August.

Based in Brittany and sponsored by the Yacht Club de Monaco, the yacht was built for the 2016-17 single-handed, round-the-world Vendee Globe race and is made with solar panels and underwater turbines, creating zero-carbon electricity.

The club said on its Facebook page that it is “honoured to be able to sail Greta Thunberg emission-free over the Atlantic”.

During the two-week journey, Thunberg will be accompanied by her father, Svante; the yacht’s skipper, Borris Hermann; a filmmaker; and Pierre Casiraghi, the grandson of Monaco’s late Prince Rainier III and US actress Grace Kelly.

After arriving in New York, where she will take part in several meetings and protests, Thunberg aims to travel by train and bus to the annual UN climate conference in the Chilean capital, with stops in Canada, Mexico and other countries.

Her father told the Financial Times in February that the family had bought an electric car and stopped flying when his daughter was 11 years old - a “rule that effectively ended Thunberg’s opera-singer mother’s international career”, notes the newspaper.

But while increasing numbers of people worldwide are following their lead in adopting greener lifestyles, Thunberg told AP that she is not sure how her message will be received in the US. Meeting with President Donald Trump, who opposes the radical measures that scientists say are required to limit global warming, would be “just a waste of time”, she added.

“I have nothing to say to him,” she continued. “He obviously doesn’t listen to the science and the scientists. So why should I, a child with no proper education, be able to convince him?”

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Travis Kelce Just Landed in Sydney to See Taylor Swift

preview for How Taylor Swift Went from Country Sweetheart to Icon

At 5:33 P.M., Page Six revealed that Kelce landed in Sydney around 5 P.M. ET/9 A.M. local time. Australian news outlets obtained footage of him leaving the plane in a navy tracksuit.

Multiple sources with direct knowledge told TMZ while Kelce was traveling what his flight route ended up being. He spent time in Las Vegas yesterday before traveling to Los Angeles. He flew to Hawaii overnight, where he continued early this morning on a private jet to Sydney.

TMZ was told that Kelce had dinner at Nobu Malibu in Los Angeles before flying to Hawaii.

Fans speculated that Kelce could be joining Swift in Australia when they noticed her private jet dropped her off in Melbourne, then returned to Hawaii . They theorized the plane could be waiting there for Kelce, which seems to be the case.

TMZ wrote that it is unclear at this point whether Kelce will just join Swift in Australia or if he will travel with her to Singapore, where she will be doing three shows next week. Once Swift wraps her Singapore show, she will be on break until she plays in Paris, France, on May 9. That opening gives Swift and Kelce the chance to make their Met Gala debut in New York City the week before.

Kelce teased he could be meeting Swift in Australia ahead of the Super Bowl. “I’m not planning anything after this Super Bowl,” he said. “I’m just focused on this game right now. But I’d love to experience down under.”

Earlier this month, a source told People that Kelce and Swift are planning to travel together for her Europe shows, too. “[They] are making plans for the summer and are excited to travel together in Europe when Taylor takes her tour there,” the insider said.

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Mary’s Long Journey to Visit Elizabeth: Exploring How Far She Traveled

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By Happy Sharer

where did she travel

Introduction

The story of Mary and Elizabeth is a timeless tale of family, faith, and friendship. In the Bible, Mary travels from Nazareth to visit her cousin Elizabeth in Judea. But just how far did Mary travel to see Elizabeth? In this article, we will explore the distance Mary covered on her journey, the challenges she faced and overcame, and the impact her travels had on her life.

A Journey Across the Country: Mary’s Long Trip to Visit Elizabeth

When Mary set off on her journey, she was embarking on a long and difficult trip. There were no cars or planes to help her get there faster—she had to rely on her own two feet. She also had to plan her route carefully, taking into account the terrain, the resources available, and the time it would take to reach her destination.

Planning the Route

To begin her journey, Mary had to decide which route she would take. She could travel east through Samaria, or she could go south around the Dead Sea. Each route presented its own challenges and opportunities. For example, traveling east meant going through hostile territory, but it would be shorter than the southern route. In the end, Mary chose the longer route, opting for safety over speed.

The Challenges of Long-Distance Travel

Once Mary had chosen her route, she had to face the challenges of long-distance travel. She had to find food, water, and shelter along the way, as well as navigate unfamiliar terrain. She also had to contend with the elements, as the weather could change quickly and unexpectedly. All of these factors added up to make Mary’s journey more difficult and dangerous.

Taking into Account Time and Resources

Finally, Mary had to take into account the time and resources she had available. She had to complete her journey as quickly as possible so that she could return home before her pregnancy became too advanced. At the same time, she had to ensure that she had enough food and water to last her the entire trip. It was a delicate balance between speed and sustainability.

Exploring the Distance: How Far Did Mary Travel to See Elizabeth?

Now that we have discussed the challenges Mary faced on her journey, let’s explore the distance she traveled. To estimate the miles Mary covered, we can look at the maps of her route. The total distance from Nazareth to Judea is approximately 90 miles, though the exact number depends on the route taken.

Estimating the Miles

We can use Google Maps to determine the approximate distance Mary traveled. Using the ‘Get Directions’ feature, we can plot out a route from Nazareth to Judea. According to Google Maps, the total distance is 91 miles. This gives us an idea of how far Mary traveled on her journey.

Calculating the Time Needed

In addition to estimating the miles Mary covered, we can also calculate the amount of time it would have taken her to complete her journey. Assuming she traveled at a walking pace of 3 miles per hour, it would have taken her approximately 30 hours to cover the 91-mile distance. That means Mary spent about one and a half days making her way to Judea.

Charting the Course: Mapping Mary’s Excursion to Visit Elizabeth

Now that we have estimated the distance Mary traveled, let’s map out her journey. We can use historical maps to trace her route from Nazareth to Judea. These maps show us the various towns, roads, and rivers Mary encountered along the way.

Examining the Maps

By examining the maps, we can get a clearer picture of Mary’s journey. The maps tell us the approximate routes she took and the places she stopped along the way. We can also see the landmarks she passed, such as the Jordan River and the Sea of Galilee. This gives us a better understanding of the terrain she encountered during her travels.

Creating a Detailed Itinerary

Using the maps, we can create a detailed itinerary for Mary’s journey. We can list out the different towns she visited, the roads she took, and the landmarks she passed. This helps us understand the full scope of her travels and gives us insight into the challenges she faced along the way.

An Adventure Awaits: Mary’s Long Trek to Elizabeth

Now that we have mapped out Mary’s journey, let’s explore the adventure that awaited her. As she began her trek, she had to prepare for the long and arduous journey ahead. She had to gather supplies, pack her bags, and make sure she had enough food and water to last her the entire trip.

Preparing for the Trip

Before setting off, Mary had to make sure she was ready for the journey ahead. She had to gather supplies, such as food, water, and clothing, and pack them in her bag. She also had to make sure she had enough money to cover any expenses along the way. Finally, she had to make sure she had a plan for where she would stay each night.

Overcoming Obstacles Along the Way

As Mary made her way across the country, she encountered many obstacles. She had to cross rivers and climb mountains, as well as deal with unfriendly locals and harsh weather. She also had to contend with fatigue and hunger, as there were no rest stops along the way. Despite all these challenges, Mary persevered and eventually reached her destination.

Crossing Borders: Mary’s Exciting Expedition to Visit Elizabeth

As Mary made her way across the country, she had the opportunity to explore new places and experience different cultures. She saw sights she had never seen before and tasted foods she had never tasted. This gave her a chance to expand her horizons and gain a greater appreciation for the world around her.

Visiting New Places

Along the way, Mary visited many new places. She stopped in villages and towns she had never seen before and got to know the people who lived there. She also encountered different customs and traditions, giving her a better understanding of the cultures she encountered.

Experiencing Different Cultures

Mary also had the chance to experience different cultures first-hand. She met people from different backgrounds and heard stories of their lives. This gave her a deeper appreciation for the diversity of the world around her and showed her how interconnected we all are.

A Tale of Two Cities: Mary’s Epic Quest to See Elizabeth

After weeks of traveling, Mary finally reached her destination. She arrived in Judea and was greeted by her cousin Elizabeth. This marked the end of Mary’s epic journey and the beginning of a lifelong friendship between the two women.

Reaching the Destination

When Mary arrived in Judea, she was welcomed with open arms. Elizabeth was overjoyed to see her and embraced her with love and kindness. After months of travel, Mary had finally reached her destination.

Reflecting on the Journey

As Mary reflected on her journey, she realized how much she had learned and grown. She had seen new places, experienced different cultures, and made friends along the way. Most importantly, she had gained a greater appreciation for the world around her.

Mary’s journey to visit Elizabeth was an epic quest filled with obstacles and challenges. She traveled an estimated 91 miles, facing many difficulties along the way. Despite the hardships, Mary persevered and eventually reached her destination. Through her travels, she gained a greater appreciation for the world around her and forged a lifelong bond with her cousin Elizabeth.

Summary of Mary’s Journey

In summary, Mary traveled an estimated 91 miles from Nazareth to Judea. She faced many challenges along the way, but ultimately overcame them and reached her destination. Through her journey, she gained a greater appreciation for the world around her and formed a strong bond with her cousin Elizabeth.

How Far Did Mary Travel to Visit Elizabeth?

To answer the question of how far Mary traveled to visit Elizabeth, we can estimate that she covered a total distance of 91 miles. This journey took her approximately 30 hours to complete and was filled with challenges and adventures. Mary’s journey was an epic quest that changed her life and taught her many valuable lessons.

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Hi, I'm Happy Sharer and I love sharing interesting and useful knowledge with others. I have a passion for learning and enjoy explaining complex concepts in a simple way.

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In Russia’s Arctic, Alexei Navalny’s mother searches for her son’s body

Detentions were being made in Moscow as residents laid flowers at the monument to political prisoners following the announcement of news of imprisoned opposition leader Alexei Navalny’s death in a Russian prison. (Feb 16).

A policeman guards as a young man lay flowers paying the last respect to Alexei Navalny at the monument, a large boulder from the Solovetsky islands, where the first camp of the Gulag political prison system was established, near the historical the Federal Security Service (FSB, Soviet KGB successor) building, in Moscow, Russia, on Saturday morning, Feb. 17, 2024. Russian authorities say that Alexei Navalny, the fiercest foe of Russian President Vladimir Putin who crusaded against official corruption and staged massive anti-Kremlin protests, died in prison. He was 47. (AP Photo/Alexander Zemlianichenko)

A policeman guards as a young man lay flowers paying the last respect to Alexei Navalny at the monument, a large boulder from the Solovetsky islands, where the first camp of the Gulag political prison system was established, near the historical the Federal Security Service (FSB, Soviet KGB successor) building, in Moscow, Russia, on Saturday morning, Feb. 17, 2024. Russian authorities say that Alexei Navalny, the fiercest foe of Russian President Vladimir Putin who crusaded against official corruption and staged massive anti-Kremlin protests, died in prison. He was 47. (AP Photo/Alexander Zemlianichenko)

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For the mother of Alexei Navalny , the Russian opposition leader who died at age 47 in an Arctic penal colony, the journey to recover her son’s body Saturday was an odyssey with no clear destination.

In the end, she didn’t get what she came for.

Lyudmila Navalnaya, 69, received an official note Saturday stating that the politician had died in prison at 2:17 p.m. local time a day earlier, Kira Yarmysh, Navalny’s spokesperson said Saturday.

Together with members of Navalny’s legal team, Lyudmila traveled to the town of Kharp in the Yamalo-Nenets region, some 1,900 kilometers (1,200 miles) northeast of Moscow.

Flowers and a photo of Russian opposition leader Alexei Navalny are placed near the Russian consulate in Frankfurt, Germany, Saturday, Feb. 17, 2024. Navalny, who crusaded against official corruption and staged massive anti-Kremlin protests as President Vladimir Putin's fiercest foe, died Friday in the Arctic penal colony where he was serving a 19-year sentence, Russia's prison agency said. He was 47. (AP Photo/Michael Probst)

It was there that Russia’s Federal Penitentiary Service said Friday that Navalny felt unwell after a walk and fell unconscious. When Lyudmila arrived less than 24 hours later, officials said that her son had died from “sudden death syndrome,” said Ivan Zhdanov, the director of Navalny’s Anti-Corruption Foundation. He did not elaborate.

Navalny’s death removed the Russian opposition’s most well-known and inspiring politician less than a month before an election that will give President Vladimir Putin another six years in power .

Prison employees told Navalny’s mother Saturday that they did not have her son’s body. They said it had been taken to the nearby city of Salekhard, a little over an hour’s drive away, as part of a probe into his death.

When Lyudmila arrived in the town with one of Navalny’s lawyers, however, they found that the morgue was closed, Navalny’s team wrote on their Telegram channel. When the lawyer called the morgue, they were told that the politician’s body was not there either.

This time, Lyudmila headed directly to Salekhard’s Investigative Committee office. A small group of journalists watched as Lyudmila walked toward the office, dressed in a thick black coat as temperatures hovered close to minus 25 degrees centigrade (minus 13 degrees Fahrenheit). Occasionally, she took the arm of one of those walking next to her as the group made their way along paths edged with thick piles of snow.

Here, she was told that the cause of her son’s death had, in fact, not yet been established, said Navalny’s spokesperson, Kira Yarmysh. Officials told Lyudmila that the politician’s relatives would not receive his body until they had completed additional examinations.

Initially, it seemed as if Lyudmila might head to another morgue. Instead, she returned to her hotel in the town of Labytnangi, another 30-minute drive. Navalny’s team, meanwhile, said they were still no closer to finding out where the politician’s body was being held.

“It’s obvious that they are lying and doing everything they can to avoid handing over the body,” Yarmysh wrote on X, formerly known as Twitter, after Lyudmila’s visit to the Investigative Committee office. The spokesperson also said that Navalny’s team “demand that Alexei Navalny’s body be handed over to his family immediately.”

Navalny, who had been serving a 19-year prison term since January 2021 after being convicted three times for extremism, has spoken several times about whether he might die while in custody.

After the last verdict, which Navalny believed to be politically motivated, he said that he understood he was “serving a life sentence, which is measured by the length of my life or the length of life of this regime.”

where did she travel

Kyrsten Sinema trails far behind in the polls. Can she make a comeback in Senate race?

where did she travel

U.S. Sen. Kyrsten Sinema has kept her political future a closely guarded secret, repeatedly sidestepping questions about whether she plans to seek a second term.

She has until April 1 to turn in more than 42,000 signatures from eligible voters to qualify for the ballot, meaning her official decision won’t be postponed much longer.

But there is another element to the decision that may be just as important: Could she even win again?

Sinema, I-Ariz., is consistently finishing third in polls of the race, sometimes by more than 20 percentage points behind either Democrat Ruben Gallego, a U.S. representative, or Republican Kari Lake, a former TV news anchor. Voting in Arizona will begin in early October, meaning a comeback, if there is to be one, must get underway quickly.

Political comebacks are an inexact science, but there are few prominent examples of anyone winning a federal race in recent memory after trailing by double digits with less than eight months to go before voting begins.

Prep for the polls: See who is running for president and compare where they stand on key issues in our Voter Guide

That is what Sinema faces.

A Sinema spokesperson declined to comment, noting that she remains focused on the work of a senator.

The Arizona Republic asked political experts for examples of comebacks — or polling misses that got the outcome as wrong as Sinema now needs it to be. They struggled to find anything that seems to apply.

“Absent a scandal, not really,” said Jessica Taylor, who edits Senate and gubernatorial races for the nonpartisan Cook Political Report. “But we also are at a point where I think the electorate is not fully engaged. So, I do think polls this early have to be taken with a grain of caution.”

Matt Grossman, a political science professor at Michigan State University, said, “Nothing jumps to mind,” when asked for such an example.

Grossman noted that Texas billionaire Ross Perot narrowly led the 1992 presidential campaign in June by some polling, only to drop out of the race, return months later and finish third to the man who was in third that summer, Arkansas Gov. Bill Clinton.

Morris Fiorina, a political science professor at Stanford University who researches public opinion and elections, had a similar answer.

He noted that Massachusetts Gov. Michael Dukakis led Vice President George H.W. Bush big after the Democratic National Convention in the summer of 1988 and wound up losing.

“For Senate, the biggest recent surprise was (Sen. Susan Collins, R-Maine) winning by 8 points after some polls had her down double digits,” Fiorina wrote in an email to The Republic. That 2020 victory over Democrat Sara Gideon came despite being heavily outspent.

Barrett Marson, a Republican campaign consultant, cautioned against writing off Sinema too quickly. For one, she still has the largest cash war chest at more than $10 million.

“She may be behind, but she has a lot of money to spend … and she has a true record of accomplishments,” he said. “Now, do voters care about records of accomplishment? I guess we’ll find out.”

Sinema has been one of the most consequential senators in Washington in recent years. She played a leading role in a national infrastructure spending plan, adding scrutiny to gun sales for younger adults and potential money for mental health care, and she was the last vote to secure President Joe Biden’s domestic agenda, which happened when she preserved lighter tax treatment for financial managers and extra money for drought mitigation in the Southwest.

More recently, Sinema helped broker a bipartisan bill to boost resources along the border with Mexico that included foreign or military aid to Ukraine, Israel and Taiwan. That deal fell apart after former President Donald Trump urged Republicans to reject it.

There isn’t a lot of publicly available polling in Arizona’s Senate race to this point, and they reflect the slow-to-form candidate field.

Sinema, who won in 2018 as a Democrat, hasn’t announced her plans, and Lake, the Republican front-runner, only entered the race in October after months of anticipation that she would do so.

The politics website FiveThirtyEight.com lists eight polls for the Arizona Senate race since Lake entered the contest. Of the six that included Sinema, she trailed by an average of more than 17 percentage points. That showing was outside the margin of error in each of the polls.

Lake recently has shown a narrow lead over Gallego in polls done by left- and right-leaning firms.

Sinema's best showing came in a pair of polls by the same organization taken in October that showed her getting 32% support in the only poll released so far featuring Pinal County Sheriff Mark Lamb as the GOP nominee.

In the other four polls with Sinema, taken by left- and right-leaning organizations, she didn’t get more than 17% support against Lake and Gallego.

Seeking support: Sen. Kyrsten Sinema rails on Republicans, then turns to GOP fundraisers for help

“Independents in general have a hard time,” said Don Ritchie, the U.S. Senate historian emeritus. “We’ve been stuck with a two-party system for such a long time that it’s hard to break out of that mold.”

He pointed to the 1980 presidential race in which John Anderson, an independent from Illinois, appeared strong in some polling, only to get less than 7% of the actual vote.

That isn’t surprising, Grossman said.

“Anytime there’s a three-candidate race, it usually means we expect more volatility,” he said. “Typically, it would mean the third-party candidate would lose support as we get closer to Election Day, but that is because voters want to be involved in making the decision between the two most likely candidates.”

In Sinema’s case, if the public believes she is trailing badly, it could make it harder for her to win as an independent over those who worry about wasting their vote.  

If Sinema does hope to keep her seat, she must climb not only past one rival, but two, a reality that adds even more complexity to the task.

The Recount: This court decision could transform how Arizona votes

Her fundraising has fallen three quarters in a row, while her Democratic and Republican challengers figure to inherit significant financial aid and campaign help from their respective parties as the contest heats up.

Sinema is also very well known to voters, suggesting that most have already formed an opinion of her that could be hard to change.

Taylor said, “Ruben Gallego is less of a known entity, so he has maybe more of an opportunity to introduce himself. But he’s still very well known within Maricopa (County). That’s going to be the majority of the vote, so I think it’s hard.”

I'm afraid of flying but travel anyway. Here are 3 things that help combat my aerophobia.

  • For years I suffered from severe fear of flying. 
  • I would get anxiety, body shakes, and diarrhea while traveling by plane. 
  • Three small changes made flying more bearable for me. 

Insider Today

My family travels several times a year: visiting relatives in California, Montana , and Massachusetts; vacations to beaches and national parks; college visits with our teenage sons; weddings; memorial services.

For 30 years, however, I've suffered from a severe fear of flying . I can fly, but getting on an airplane involves hours of full-body shaking, extreme diarrhea , and overwhelming anxiety coupled with dark bouts of depression leading up to any flight.

It appeared out of nowhere

This fear, as irrational as it is debilitating , appeared suddenly, soon after I graduated from college. As a young person, I would have put travel-lover as my top self-defining feature, but the more years that passed since my fear of flying began, the less I sought out travel opportunities.

It's certainly limited how my husband and I explore the world with our children and even limited how often I see family or friends. I missed my stepfather's 50th birthday celebration because I couldn't get on the plane .

People always want to know whether a traumatic experience set off this fear, but it wasn't like that. Yes, I've been in bad weather in small planes that have needed emergency clearance to land. And once, while visiting family in India, we flew through a monsoon; our pilot made the situation so much worse by announcing at regular intervals that their competitor airline had to make emergency landings while our poor plane was thrown up, down, and sideways.

Honestly, my least favorite flight is the one I do most often, between Pittsburgh and Boston. The weather is never quite right, and the 75 minutes in the air is just a bit too long for me as a "short flight."

I did so many things before flying

The strategies I used to depend on were based on manufacturing control over things out of my control. Strategies like checking the weather sites hourly leading up to a trip. Or asking the flight attendant immediately upon boarding whether they were expecting turbulence. I always bought window seats and stared out the window at the wing for every second in the air, as if my concentration and vigilance were the only things keeping the plane aloft.

When we'd land, I was flooded with the most euphoric adrenaline — like I'd just won an Olympic medal — because I had done this thing that most people do without any concern or effort. Unless you share this phobia, you have no idea what each flight cost me.

Thirty years is a long time to feel terrified about something so mundane and safe. A few years ago, I sought out a therapist to help me with this struggle. He asked me what I was so afraid of, and I told him it was imagining those long moments when the plane was plummeting to the ground. I didn't think I could face them. What he said in response changed my life.

"You are in control of what you do with those terrible last minutes," he said.

Here are 3 things that have helped me control my fear of flying

Friends and family like to list statistics for me. I know flying is safer than driving. I know the number of flights per day around the world is ridiculously large, and all those passengers and crew arrive at their destinations without harm. But that's the thing about irrational fears: rational reasoning doesn't help.

What I needed — and received from a single session with that therapist — was a sense of control. So here's what I learned and what's been a game changer for me.

I know that if the plane goes down, while I have no control over the outcome, I have control over how I spend those last moments. I can hug my loved ones if they're with me. If I'm alone, I can wrap my arms tightly around myself and fill my mind with images of those people I love most: my husband and two children.

Instead of interpreting the physical symptoms of anxiety as signs of actual danger, I can name them for what they are: My legs are shaking. I'm lightheaded. I feel sick to my stomach.

When the plane bounces through turbulent air, I tell myself, "I feel scared, but what I'm doing is actually very safe."

It's not that I now fly worry-free. But I pay little attention to the weather, and I no longer sink into doomsday darkness during the days leading up to a trip. I still get diarrhea, but Imodium helps. On some flights, I'm able to read or listen to music. I still stare out the window, but it has nothing to do with holding up the plane; instead, it's how I pass the time, studying the clouds or watching the changing landscape below. If I have room in my carry-on, I pack a small blanket to pull snugly over my lap. Sometimes, I find peace with the turbulence.

These are small changes. They've made a huge impact on my life.

where did she travel

Watch: Why you shouldn't be afraid to fly, according to a pilot with over 20 years of experience

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  26. DA Fani Willis testified she paid cash during trips with top ...

    After spending more than two hours tasting wine at a Napa Valley estate with her top prosecutor on the Georgia election subversion case, Fulton County District Attorney Fani Willis reached into ...

  27. Alexei Navalny: Mother denied access to morgue where body was believed

    For the mother of Alexei Navalny, the Russian opposition leader who died at age 47 in an Arctic penal colony, the journey to recover her son's body Saturday was an odyssey with no clear destination.. In the end, she didn't get what she came for. Lyudmila Navalnaya, 69, received an official note Saturday stating that the politician had died in prison at 2:17 p.m. local time a day earlier ...

  28. Arizona Senate race: If Kyrsten Sinema runs, can she win?

    Sinema, I-Ariz., is consistently finishing third in polls of the race, sometimes by more than 20 percentage points behind either Democrat Ruben Gallego, a U.S. representative, or Republican Kari ...

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