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Math Help - Race and time problem.

  1. #1
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    Race and time problem.

    In a km race, if A gives B a 40 m start, A wins by 19 seconds, but if A gives B 30 seconds start, B wins by 40 m. Find the time that each takes to run a km?
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  2. #2
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    Re: Race and time problem.

    This is just algebra, isn't it? Let t_A be A's time for a kilometer and t_B be B's time for a kilometer. Then the first condition is:

    t_A = 0.96t_B - 19

    The second condition is:

    0.96t_A = t_B-30

    So the solution is t_B=150, t_A=125, i.e. A takes 125 seconds to run a kilometer and B takes 150 seconds to run a kilometer.

    - Hollywood
    Last edited by hollywood; December 20th 2012 at 08:27 AM. Reason: Latex
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  3. #3
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    Re: Race and time problem.

    Sorry for the late response. can you explain in details how do you get to those equations.
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  4. #4
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    Re: Race and time problem.

    It's pretty much just translating the words to equations. It's actually not easy - you have to think about what's happening in these races:

    "if A gives B a 40 m start, A wins by 19 seconds"
    so A runs 1km in 19 seconds less time than B runs 0.96km
    t_A = 0.96t_B - 19

    "if A gives B 30 seconds start, B wins by 40 m"
    so A runs 0.96km in 30 seconds less time than B runs 1km
    0.96t_A = t_B-30

    - Hollywood
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