Question

In still water Kevin and Virginia can paddle a canoe at 12mph.It takes them a total of 6hours to paddle 32 miles up a river and then return the same distance to their starting point. What is the rate of the current?

Answer 1

Let c represent the speed of the current.

time = distance/speed

Upriver, the current is subtracted from the canoe speed; downriver, it adds.
6 = 32/(12 -c) +32/(12 +c)
6(12² -c²) = 32(12 +c) +32(12 -c) . . . . . multiply by (12 +c)(12 -c)
0 = 6c² -96 . . . . . . . . . . . . . . . . . . . . . . subtract the left side
96/6 = c² . . . . . . . . . . . . . . . . . . . . . . . . add 96, divide by 6
4 = c . . . . . . . . . . . . . . . . . . . . . . . . . . . . take the square root

The rate of the current is 4 mph.