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Peggy rode her bike to the farm. Mike decided to go by car. It took Mike half an hour to get there. Peggy made the trip in 2 hours. How far was the farm if mike was traveling 36mph faster than Peggy?

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  1. 9 July, 23:37
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    The farm was 24 miles away.

    Step-by-step explanation:

    In order to solve this question we will attribute variables to the problem. We have:

    The speed at wich Peggy was going it'll be "v_peggy";

    The speed at wich Mike was going it'll be "v_mike".

    The distance they travelled will be "d".

    The problem told us that the speed Mike travelled was 36 mph faster than Peggy, so:

    v_mike = v_peggy + 36

    The distance of said course is given by the speed and the the time it took to complete it. So we have:

    d = 0.5*v_mike and d = 2*v_peggy

    The distances are the same, so:

    0.5*v_mike = 2*v_peggy

    Using the equation that relates Mike's speed to Peggy's, we have:

    (v_peggy+36) * 0.5 = 2*v_peggy

    0.5*v_peggy + 36*0.5 = 2*v_peggy

    2*v_peggy - 0.5*v_peggy = 18

    1.5*v_peggy = 18

    v_peggy = 12 mph

    Now we can compute the distance that is:

    d = (12) * 2 = 24 miles
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