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Math Help - river's problem..Help!

  1. #1
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    river's problem..Help!

    it takes 5 hours to travel downstream on a river from port A to port B and 7 hours to make the same trip upstream from B to A.How long would it take for a raft,which is propelled only by current of the river to get from A to B?
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  2. #2
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    Reply

    Let speed of boat = x km/h
    and speed of River Current = y km/h, (x > y)

    Speed of boat in downstream = (x + y) km/h
    Speed of boat in upstream = (x - y) km/h

    Distance covered in downstream from A to B is = speed . time = 5(x + y) hours

    Distance covered in upstream from B to A is = speed . time = 5(x - y) hours

    Since, the distance is same,

    5(x + y) = 7(x - y)

    12y = 2x

    \frac{x}{y} = 6

    Since the distance covered by raft from A to B is also same.
    Distance covered by raft = 5(x + y)
    Speed of raft = speed of current = y

    Time taken by raft = \frac{Distance}{speed}

    = \frac{5(x+y)}{y}= 5\left(\frac{x}{y}+1\right)

    = 5\left(6+1\right) = 35 hours.

    It will take 35 hours by raft.
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