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30 July, 21:52

On an up hill hike Ted climbs at 3 mph. Going back down, he runs at 5 mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?

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  1. 30 July, 22:37
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    The main formula is:

    Distance traveled = (average) Speed*Time.

    i) when Ted Climbs up:

    let D be the distance, T the time it takes Ted to climb, S_u=3mph is the speed as Ted climbs up.

    then: D=3T

    ii) when Ted goes down:

    D is the distance, T-40 the time it takes Ted go down, S_d=5mph is the speed as Ted climbs up.

    then: D=5 (T-40)

    equalizing the equations in i and ii:

    (D=) 3T=5 (T-40)

    3T=5T-200

    200=2T

    T=100 (minutes)

    the total length of the hike is T+T-40=100+100-40=160 (minutes)

    Answer: 160 minutes
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