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13 January, 12:13

a jogger runs 4 miles per hour faster downhill than uphill. if the jogger can run 5 miles downhill in the same time that it takes to run 3 miles uphill, find the rate in each direction

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  1. 13 January, 12:58
    0
    Downhill: 10 miles/hour

    Uphill: 6 miles/hour

    Step-by-step explanation:

    (5/t) - (3/t) = 4

    2/t = 4

    t = ½

    Downhill: 5/½ = 10 miles/hour

    Uphill: 3/½ = 6 miles/hour
  2. 13 January, 13:20
    0
    Answer: the rate uphill is 6 mph.

    The rate downhill is 10 mph

    Step-by-step explanation:

    Let x represent the rate at which the jogger ran uphill.

    The jogger runs 4 miles per hour faster downhill than uphill. This means that speed at which the jogger ran downhill is (x + 4) mph

    Time = distance/speed

    if the jogger can runs 5 miles downhill, then the time taken to run downhill is

    5 / (x + 4)

    At the same time, the jogger runs 3 miles uphill. It means that the time taken to run uphill is

    3/x

    Since the time is the same, it means that

    5 / (x + 4) = 3/x

    Cross multiplying, it becomes

    5 * x = 3 (x + 4)

    5x = 3x + 12

    5x - 3x = 12

    2x = 12

    x = 12/2

    x = 6

    The rate downhill is 6 + 4 = 10 mph
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