A CRUISE BOAT TRAVELS 96 MILES DOWNSTREAM IN 4 HOURS AND RET

A CRUISE BOAT TRAVELS 96 MILES DOWNSTREAM IN 4 HOURS AND RETURNS TO ITS STARTING POINT UPSTREAM IN 12 HOURS. FIND THE SPEED OF THE STREAM.

Solution

Let s = speed of the boat in still water
Let c = speed of the stream
then
(s+c) = speed downstream
(s-c) = speed upstream
:
Write a distance equation for each trip; dist = time * speed
:
4(s +c) = 96
12(s-c) = 96
:
Simplify, divide the 1st equation by 4 and the 2nd equation by 12
s + c = 24
s - c = 8
-------------subtraction eliminates s, find c:
2c = 16
c = 8 mph, speed of the stream, (which is what they asked for)
:
:
To check solution find the speed of the boat
s - 8 = 8
s = 16 mph, speed of the boat