Suppose there is a river of width 100 feet. Both swimmers swim at the same speed of 5 ft per second. The river is flowing at a rate of 3 feet per second.

Both swimmers start at the same point.

Swimmer A: swims to a point directly across on the opposite side, then turns around and swims back to the starting point.

Swimmer B: stays on one side of the river, and swims upstream a distance exactly equal to the width of the river, then swims back to the starting point.

Which swimmer wins the race and why?

Okay, if you make a picture of the situation, you'll get everything very easily.

River flow-rate = 3 ft/s

Swimmer A's resultant speed so that he travels in a straight line to the other bank is:

v = \sqrt{5^2 - 3^2} = 4\ ft/s

This is his speed during all the race.

Swimmer B's resultant speed upstream is 5 - 3 = 2 ft/s
His speed downstream is 5 + 3 = 8 ft/s

Find the time it takes for both swimmers to get back to the starting point, given the distance is 100 ft for the first part, and another 100 ft for the return part.

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