Question

A power boat travels along a river in which the flow of water is at a constant in one direction. If the boat travels at 40 mph downstream and 30 mph upstream. What is the speed of the boat in still water and the speed of the river?

Answer 1

speed of boat is 35 mph

speed of river is 5mph.

Explanation:

Let the speed of boat be u mph

let the speed of river be v mph

When boat travel downstream

in that case flow of river will support the speed of boat hence

speed of river will be added to speed of boat

Thus,

speed of boat in downstream = speed of boat + speed of river = u + v

Given

the boat travels at 40 mph downstream

thus,

u + v = 40 -----1

When boat travel upstream

in that case flow of river will oppose the speed of boat hence

speed of river will be subtracted from speed of boat

Thus,

speed of boat in downstream = speed of boat -speed of river = u - v

Given

the boat travels at 30 mph upstream

thus,

u - v = 30 ----2

adding 1 + 2

we have

u + v = 40

+ u - v = 30

2u = 70

u = 70/2 = 35

Thus,

speed of boat is 35 mph

using u = 35 in u + v = 40

we have

35 + v = 40

v = 40 - 35 = 5

Thus, speed of river is 5mph.