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1.4 Units & Conversions

1.4 Units & Conversions
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  • 7. Finding Travel Time

    The road sign shows your distance to several nearby cities in miles. You are driving at 45 miles per hour. Which of the following expressions should you use to determine how long it will take to get to Ventura? How long will it take? (See Example 3.)

    • Worked-Out Solution

      You can use unit analysis to see which expression is correct.

      The only one that makes sense is (b).

      It will take you an hour and 12 minutes to get to Ventura.

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      _  _     _____     _  __     ___     _____    
     | \| ||  |  ___||  | |/ //   / _ \\  |  __ \\  
     |  ' ||  | ||__    | ' //   / //\ \\ | |  \ || 
     | .  ||  | ||__    | . \\  |  ___  ||| |__/ || 
     |_|\_||  |_____||  |_|\_\\ |_||  |_|||_____//  
     `-` -`   `-----`   `-` --` `-`   `-`  -----`   
                                                    
    
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  • 8. Finding Travel Time

    The road sign shows your distance to several nearby cities in miles. You are driving at 65 miles per hour. How long will it take to get to Los Angeles? (See Example 3.)

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    __    __     ___       _____    ______    _  __  
    \ \\ / //   / _ \\    / ___//  /_   _//  | |/ // 
     \ \/ //   / //\ \\   \___ \\   -| ||-   | ' //  
      \  //   |  ___  ||  /    //   _| ||_   | . \\  
       \//    |_||  |_|| /____//   /_____//  |_|\_\\ 
        `     `-`   `-` `-----`    `-----`   `-` --` 
                                                     
    
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  • 9. Weight of a Human Heart

    How much does a heart weigh in pounds? (See Example 3 and Example 4.)

    • Worked-Out Solution

      The weight is given in ounces. You need to convert ounces to pounds.

      A human heart weighs about 0.625 pound.

      The weight of the average human heart is 10-12 ounces for a male and 8-10 ounces for a female. The weight increases with age. Some humans, like athlete Lance Armstrong, have hearts that are considerably larger than the average. This increased size allows their hearts to pump more oxygen to their bodies and consequently allows them to perform with greater endurance.

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     _    _    _    _      _____     ___      ______  
    | \  / || | || | ||   / ___//   / _ \\   /_   _// 
    |  \/  || | || | ||   \___ \\  / //\ \\    | ||   
    | .  . || | \\_/ ||   /    // |  ___  ||  _| ||   
    |_|\/|_||  \____//   /____//  |_||  |_|| /__//    
    `-`  `-`    `---`   `-----`   `-`   `-`  `--`     
                                                      
    
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  • 10. Comparing a Human's Brain to Heart

    A human brain weighs about 3 pounds. How many ounces heavier is a brain than a heart? (See Example 3 and Example 4.)

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      _  __     ___     _    _     ______     _____  
     | |/ //   / _ \\  | |  | ||  /_   _//   / ___// 
     | ' //   | / \ || | |/\| ||   -| ||-    \___ \\ 
     | . \\   | \_/ || |  /\  ||   _| ||_    /    // 
     |_|\_\\   \___//  |_// \_||  /_____//  /____//  
     `-` --`   `---`   `-`   `-`  `-----`  `-----`   
                                                     
    
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  • 11. Pumping Capacity of a Human Heart

    How many quarts of blood does a heart pump in 1 minute? (See Example 3 and Example 4.)

    • Worked-Out Solution

      You can use unit analysis to answer this question. This is like solving a puzzle. You need to find fractions to multiply so that the result is quarts per minute.

      A human heart pumps about 5.47 quarts of blood per minute.

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      ______    ______   __   _    __   __   _    _   
     /_   _//  /_   _// | || | ||  \ \\/ // | |  | || 
     `-| |,-    -| ||-  | '--' ||   \ ` //  | |/\| || 
       | ||     _| ||_  | .--. ||    | ||   |  /\  || 
       |_||    /_____// |_|| |_||    |_||   |_// \_|| 
       `-`'    `-----`  `-`  `-`     `-`'   `-`   `-` 
                                                      
    
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  • 12. Pumping Capacity of a Human Heart

    How many gallons of blood does a heart pump in 1 day? (See Example 3 and Example 4.)

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     __   _    _    _     ____       ___     _    _   
    | || | || | || | ||  |  _ \\    / _ \\  | \  / || 
    | '--' || | || | ||  | |_| ||  / //\ \\ |  \/  || 
    | .--. || | \\_/ ||  | .  //  |  ___  ||| .  . || 
    |_|| |_||  \____//   |_|\_\\  |_||  |_|||_|\/|_|| 
    `-`  `-`    `---`    `-` --`  `-`   `-` `-`  `-`  
                                                      
    
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  • 13. Estimating the Length of a Heartbeat

    A patient's heart rate can be determined from an electrocardiogram (EKG). The time between two peaks on the EKG represents one heartbeat. Ringo Starr sang a song that had the words "In a heartbeat, I'll be by your side." What is the length of one heartbeat? (See Example 4.)

    • Worked-Out Solution

      Using the graph, the distance between two dark grid lines represents 0.2 second. There are about 4 of these distances between the two peaks. So, the time between the two peaks is

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     _    _    __   __   _    _      ___      ____    
    | \  / ||  \ \\/ // | \  / ||   / _ \\   |  _ \\  
    |  \/  ||   \ ` //  |  \/  ||  | / \ ||  | |_| || 
    | .  . ||    | ||   | .  . ||  | \_/ ||  | .  //  
    |_|\/|_||    |_||   |_|\/|_||   \___//   |_|\_\\  
    `-`  `-`     `-`'   `-`  `-`    `---`    `-` --`  
                                                      
    
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  • 14. Estimating Heart Rate

    A patient's heart rate can be determined from an electrocardiogram (EKG). The time between two peaks on the EKG represents one heartbeat. What is the heart rate of the person whose EKG is shown? Is the heart rate shown normal? (See Example 4.)

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      _____    _    _     _____    _    _    __   __  
     |__  //  | || | ||  /  ___|| | || | ||  \ \\/ // 
       / //   | || | || | // __   | || | ||   \   //  
      / //__  | \\_/ || | \\_\ || | \\_/ ||   / . \\  
     /_____||  \____//   \____//   \____//   /_//\_\\ 
     `-----`    `---`     `---`     `---`    `-`  --` 
                                                      
    
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