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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- Oct 20th 2008, 12:09 PMfranckherve1river'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?

- Oct 20th 2008, 12:32 PMShyamReply
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

$\displaystyle \frac{x}{y} = 6$

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 $\displaystyle = \frac{Distance}{speed}$

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

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

It will take 35 hours by raft.