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Math Help - Linear Equations?

  1. #1
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    Linear Equations?

    Chris walks at 8 km/h and runs at 12 km/h. One day he walks and runs on the way from his house to the library. It takes him 20 minutes. On his way back from the library he runs twice as far and the journey home takes 17 1/2 minutes. How far is his house from the library?

    I've tried multiple formulas and they don't seem to work.

    I made:

    x = walking distance
    y = running distance

    8x + 12y = 20

    And every time I solve it, I get the wrong answer. My book says it's 3 km but I don't know how to get there. Help would be appreciated!
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  2. #2
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    Quote Originally Posted by slategray View Post
    Chris walks at 8 km/h and runs at 12 km/h. One day he walks and runs on the way from his house to the library. It takes him 20 minutes. On his way back from the library he runs twice as far and the journey home takes 17 1/2 minutes. How far is his house from the library?
    on the way back ...

    17.5 min = 7/24 hr

    Let t = walk time in hrs

    (7/24) - t = run time in hrs

    walks 1/3 of the distance ...

    d/3 = 8t ... double this, you get 2d/3 = 16t

    runs 2/3 of the distance ...

    2d/3 = 12[(7/24) - t]

    equate the run distances ...

    12[(7/24) - t] = 16t

    (7/2) - 12t = 16t

    7/2 = 28t

    t = 7/56 = 1/8 hr

    d/3 = 8t

    d = 24t = 24(1/8) = 3 km
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