Consider the swimmer in the figure below. Suppose that his swimming speed relative to the water is 5.7 m/s, current = 2.2 m/s, and that the river is 10 m wide. How long will it take for him to cross the river?
For every 5.7 m that the swimmer travels in a line perpendicular to the river bank, the current pushes him 2.2 m parallel to the river bank, so that the swimmer actually has to travel farther than 10 m to cross.
The parallel displacement can be found by setting up similar triangles:
2.2/5.7 = x/10
x = 22 / 5.7 = 3.86
The length of the hypotenuse of this triangle is (10^2 + 3.86^2)^0.5
Divide this by his speed of 5.7 m/s