Question

A river is one mile wide and the water flows at the rate 3 miles/hour. If you can paddle a canoe 5 miles/hour in still water, then how long will it take you to paddle across the river and back? How long would it take you to travel one mile upstream (measured along the bank) and back?

Answer 1

To go straight across, you would have to paddle in an upstream direction with respect to the water. The velocity component across the river would then be sqrt(5^2 - 3^2) = 4 miles/h. The time to go across and back is then
T1 = 2 mile/4 mph = 0.5 hours = 30 minutes

To go 1 mile upstreeam and then down requires
T2 = 1/(5-3) + 1/(5+3) = 1/2 + 1/8 = 5/8 hr = 37.5 minutes.