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Chapter 1 Review Exercises

Chapter 1 Review Exercises
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  • 1. Finding the Total Train Fare

    A family of six takes a one-way trip on a train. The cost is $60 per adult and $45 per child. Which of the following keystroke sequences is better for finding the total cost? Explain your reasoning.

    • Worked-Out Solution
      1. This keystroke sequence tells the calculator to add 120 and 180. This is correct.

        So, the total fare for the 6 people is $300. Note that in this situation, "a family of 6" must mean 2 adults and 4 children. Although it could have meant 1 adult and 5 children, neither of the keystroke sequences has that possibility.

      2. This keystroke sequence tells the calculator to multiply 2 by 240. This is not correct.

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      _____     ______    _  __    _____     _  __  
     /  ___||  /_   _//  | |/ //  |  ___||  | |/ // 
    | // __     -| ||-   | ' //   | ||__    | ' //  
    | \\_\ ||   _| ||_   | . \\   | ||__    | . \\  
     \____//   /_____//  |_|\_\\  |_____||  |_|\_\\ 
      `---`    `-----`   `-` --`  `-----`   `-` --` 
                                                    
    
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  • 2. Estimating Seats in a Train Car

    The seating area of a passenger car on a high-speed train is in the shape of a rectangle. It has a length of 70 feet and a width of 9 feet. Estimate how many seats can fit in the passenger car. Explain your reasoning.

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     __   _     ______   __   _      ___              
    | || | ||  /_   _// | || | ||   / _ \\    ____    
    | '--' ||   -| ||-  | '--' ||  / //\ \\  |    \\  
    | .--. ||   _| ||_  | .--. || |  ___  || | [] ||  
    |_|| |_||  /_____// |_|| |_|| |_||  |_|| |  __//  
    `-`  `-`   `-----`  `-`  `-`  `-`   `-`  |_|`-`   
                                             `-`      
    
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  • 3. Finding the Time for a Trip by High-Speed Rail

    Use the following facts about high-speed rail in China. At its top speed, about how long does it take the passenger train to travel 1050 miles?

    • In 2010, a Chinese passenger train hit a record speed of 302 miles per hour during a test run.

    • It reached the top speed on a segment of the 824-mile-long line.

    • The line is expected to open in 2012 and will halve the current travel time between the capital Beijing and Shanghai to five hours.

    • China already has the world's longest high-speed rail network, and it plans to cover 8125 miles by 2012 and 10,000 miles by 2020.

    • Worked-Out Solution

      For an estimate, you can use 300 miles per hour as the speed.

      Here is a solution using unit analysis.

       

      Here is a solution using the formula

       

      The trip will take about 3.5 hours.

      Suggestion for Math Success

      The two main things that you learned in Chapter 1 are (1) how to use unit analysis to solve problems and (2) how to calculate with percent. Once you have mastered both of these skills, you will be delighted at how much easier mathematics is.

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      _  __   __   __    _____     _____     _____   
     | |/ //  \ \\/ //  / ____||  |  ___||  / ____|| 
     | ' //    \ ` //  / //---`'  | ||__   / //---`' 
     | . \\     | ||   \ \\___    | ||__   \ \\___   
     |_|\_\\    |_||    \_____||  |_____||  \_____|| 
     `-` --`    `-`'     `----`   `-----`    `----`  
                                                     
    
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  • 4. Finding the Time for a Trip by High-Speed Rail

    Use the facts about high-speed rail in China. How long did it take to travel between Beijing and Shanghai before 2012?

    • In 2010, a Chinese passenger train hit a record speed of 302 miles per hour during a test run.

    • It reached the top speed on a segment of the 824-mile-long line.

    • The line is expected to open in 2012 and will halve the current travel time between the capital Beijing and Shanghai to five hours.

    • China already has the world's longest high-speed rail network, and it plans to cover 8125 miles by 2012 and 10,000 miles by 2020.

    Comments (0)

    These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
    When posting a comment, you agree to our Terms of Use.

      _____    __   __    _____    __   __            
     |__  //   \ \\/ //  /  ___||  \ \\/ //     ___   
       / //     \ ` //  | // __     \ ` //     /   || 
      / //__     | ||   | \\_\ ||    | ||     | [] || 
     /_____||    |_||    \____//     |_||      \__ || 
     `-----`     `-`'     `---`      `-`'       -|_|| 
                                                 `-`  
    
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  • 5. Expansion of China's High-Speed Rail System

    Use the following facts about high-speed rail in China. From 2012 to 2020, about how many miles per year does China plan to expand its high-speed rail network?

    • In 2010, a Chinese passenger train hit a record speed of 302 miles per hour during a test run.

    • It reached the top speed on a segment of the 824-mile-long line.

    • The line is expected to open in 2012 and will halve the current travel time between the capital Beijing and Shanghai to five hours.

    • China already has the world's longest high-speed rail network, and it plans to cover 8125 miles by 2012 and 10,000 miles by 2020.

    • Worked-Out Solution

      From 2012 to 2020, China plans to expand the system from 8125 miles to 10,000 miles. That is an increase of

      For the 8 years, this is an average increase of

      or about 234 miles of new track per year.

      Suggestion for Math Success

      The two main things that you learned in Chapter 1 are (1) how to use unit analysis to solve problems and (2) how to calculate with percent. Once you have mastered both of these skills, you will be delighted at how much easier mathematics is.

    Comments (0)

    These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
    When posting a comment, you agree to our Terms of Use.

     _____      _____     ______    _____    _    _   
    |  __ \\   |  ___||  /_   _//  |  ___|| | || | || 
    | |  \ ||  | ||__      | ||    | ||__   | || | || 
    | |__/ ||  | ||__     _| ||    | ||__   | \\_/ || 
    |_____//   |_____||  /__//     |_____||  \____//  
     -----`    `-----`   `--`      `-----`    `---`   
                                                      
    
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  • 6. Time for a Trip by High-Speed Rail

    Use the facts about high-speed rail in China. The track distance between Beijing and Shanghai is 819 miles. Why do you think it takes five hours to make this trip?

    • In 2010, a Chinese passenger train hit a record speed of 302 miles per hour during a test run.

    • It reached the top speed on a segment of the 824-mile-long line.

    • The line is expected to open in 2012 and will halve the current travel time between the capital Beijing and Shanghai to five hours.

    • China already has the world's longest high-speed rail network, and it plans to cover 8125 miles by 2012 and 10,000 miles by 2020.

    Comments (0)

    These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
    When posting a comment, you agree to our Terms of Use.

      ______    ______   _____     __   __            
     /_   _//  /_   _// |  __ \\   \ \\/ //     ___   
       | ||     -| ||-  | |  \ ||   \ ` //     /   || 
      _| ||     _| ||_  | |__/ ||    | ||     | [] || 
     /__//     /_____// |_____//     |_||      \__ || 
     `--`      `-----`   -----`      `-`'       -|_|| 
                                                 `-`  
    
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