Question

A cruise boat travels 48 miles Downstream in 2 hours and returns Upstream in 3 hours. Find the speed of the boat in still water and the rate of the Stream.

Answer 1

Let x be the speed of the boat in still water and y be the speed of the current of the river.
The downstream speed will be x+y, the upstream speed will be x-y.
but:
distance=speed*time
therefore; as the boat travels in 2 hours downstream we shall have:
2(x+y)=48......i
and as the boat travels upstream we shall have:
3(x-y)=48........ii
simplifying i and ii we get:
x+y=24....iii
x-y=16....iv
adding the above iii and iv we get
2x=40
x=40/2=20
substituting x=20 into iii we obtain:
20+y=24
y=24-20
y=4
so the speed of the boat in  still waters is 20 miles per hour
the rate of the stream is 4 miles per hour