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20 August, 17:12

On an uphill hike, Ted climbs at a rate of 3 miles an hour. Going down, he runs at a rate of 5 miles an hour. If it takes him 40 minutes longer to climb up than run down, what is the total length of Ted's hike?

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  1. 20 August, 17:31
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    It takes 40 minutes more going up or 40/60 = 0.67 hours more.

    Let us say that:

    t = the time required for him running down

    t + 0.67 = time required for him running up

    Since the distance of running up and down must be equal therefore:

    (3 miles / hr) * (t + 0.67) = (5 miles / h) * t

    3 t + 2.01 = 5 t

    2 t = 2.01

    t = 1.005 hr

    So the total length of the hike is:

    length = 2 * (5 miles / hr) * (1.005 hr)

    length = 10.05 miles
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