Question

It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long does it take an unpowered raft to cover this distance?

Answer 1

The answer is 192 hours

Explanation:

Answer 2

Time taken by the un powered raft to cover this distance is T = 192.12 hr

Explanation:

Let speed of boat = u
`(km)/(hr)`

Speed of current = v
`(km)/(hr)`

Let distance between A & B = 100 km

Time taken in downstream = 32 hours

`32 = (100)/(u +v)`

`u + v = (100)/(32)`

u + v = 3.125 ------ (1)

Time taken in upstream = 48 hours

`48 = (100)/(u -v)`

`u -v = (100)/(48)`

u - v = 2.084 ------- (2)

By solving equation (1) & (2)

u = 2.6045
`(km)/(hr)`

v = 0.5205
`(km)/(hr)`

Now the time taken by the un powered raft to cover this distance

`T = (100)/(v)`

Because un powered raft travel with the speed of the current.

`T = (100)/(0.5205)`

T = 192.12 hr

Therefore the time taken by the un powered raft to cover this distance is

T = 192.12 hr