# river's problem..Help!

• Oct 20th 2008, 12:09 PM
franckherve1
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?
• Oct 20th 2008, 12:32 PM
Shyam
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.