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?
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.