River is 80 ft. wide
Swimmer swims at a rate of 3.3 ft/sec
Swimmer crosses river in 20 sec.

What is the velocity of the river?

I know that isn't very much information but can you give formulas and a step-by-step solution?

This problem doesn't seem to make a lot of sense, since you'd think the swimmer would be swimming perpendicular to the current.

That being said, let's just assume the swimmer is swimming 80 ft. downstream (i.e. in the same direction as the current), not across.

The swimmer swims at 3.3 ft/sec, so how far does the swimmer go in 20 seconds?

distance = rate x time = 3.3 ft/sec x 20 sec = 66 ft.

So the swimmer covered 66 of the 80 ft on his/her own. The remaining 14 ft of distance must have be due to the current. So if the current carried the swimmer 14 extra feet in 20 seconds, how fast is it moving?

Again, distance = rate x time.

14 ft = rate x 20 sec
rate = 0.7 ft/sec

Make sense?

The other way to look at this, by the way, is to calculate the swimmer's actual speed (relative to the stationary shore), then subtract their given speed relative to the water.

Swimmer covers 80 ft in 20 seconds, so the land speed is 80/20=4 ft/sec.

Since you're told that the swimmer swims at a rate of 3.3 ft/sec (relative to the water), the current is making up the difference. 4.0 ft/sec - 3.3 ft/sec = 0.7 ft/sec.

You get the same answer either way, of course.