Find the speed of the river current.

Question

Nick knows that he can paddle his canoe a steady 3 mph in still water. At this rate, paddling in a certain river, it takes the same amount of time to travel 8 miles upstream (against the river current) as it takes to go 22 miles downstream (with the river current). Find the speed of the river current.

Answer 1

Suppose the speed of the current is c mph downstream

Then net speed upstream = (3-c) and net speed downstream = (3+c)

time upstream = 8 / (3-c)

time downstream = 22 / (3+c)

These are equal

8 / (3-c) = 22 / (3+c)

24 + 8c = 66 - 22c

30c = 66-24 = 42

c = 42/30 = 7/5 = 1.4 mph.

Check : time upstream = 8 / 1.6 = 5

time downstream = 22 / 4.4 = 5