Expert: Socrates - 1/21/2009

Question
the speed of a stream is 3km/h. A boat travels 4km upstream in the same time it takes to travel 10km downstream. What is the speed of the boat in still water? please show me step by steps how to solve this

Answer
Let s be the speed of the boat.

The stream is moving at 3km/h , so

Downstream boat speed = s+3

Upstream boat speed = s-3

Traveling downstream , the boat takes 10/(s+3) hours to travel 10 km.

Traveling upstream , the boat takes 4/(s-3) hours to travel 4 km.

We are told that these times are the same , so

10/(s+3) = 4/(s-3)

cross multiply

(10)(s-3) = (4)(s+3)

10s - 30 = 4s + 12

6s = 42

s = 7

The speed of the boat is 7 km/h