Mathematics

Question

A person drove 36 miles per hour on a trip. If he had driven 48 miles per hour he would have arrived 4 hours earlier. What was the distance the person drove?

1 Answer

  • Answer:

    d = 576

    Step-by-step explanation

    Think of the two different speeds as belonging to 2 different cars going to the same place, taking the same route and going to the same place.

    Let the time traveled by the fast car = t

    Let the time traveled by the slower car = t+4

    Let the rate of travel of the slow car = 36 mph

    Let the rate of travel of the fast car = 48 mph

    ===========

    d = 36*(t + 4)

    d = 48 * t

    Since the distance is the same, they can be equated.

    48t = 36(t + 4)           Remove the brackets.

    48t = 36t + 144          Subtract 36t from both sides.

    48t - 36t = 144           Combine

    12t = 144                     Divide by 12

    t = 144/12

    t = 12

    Therefore the faster car takes 12 hours to get where it is going.

    d = 48 * t

    d = 48 * 12

    d = 576

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