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7 November, 12:15

A salesman made a trip of 420 miles by bus and train. He traveled 3 hours by bus and 5 hours by train. If the train averaged 12 mph more than the bus, find the rate of each.

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  1. 7 November, 13:32
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    The speed at which the buss made the trip was 45 mph and the train was 57 mph.

    Step-by-step explanation:

    The average speed is given by:

    speed = distance / time

    Therefore we can manipulate it to give us the distance:

    distance = speed*time

    The time distance of each stage of his trip summed must be equal to the total distance of the trip. Since he made a trip in two legs, one by bus that lasted 3 h at a speed of "x" and one that lasted 5 hours at a speed of "x + 12". We have:

    420 = 3*x + 5 * (x + 12)

    3*x + 5 * (x + 12) = 420

    3*x + 5*x + 60 = 420

    8*x = 420 - 60

    8*x = 360

    x = 45 mph

    The speed at which the buss made the trip was 45 mph and the train was 57 mph.
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