Will is attempting to swim to a dock directly across a river from his current position. In still water he can swim at a speed of vw. The river has a speed of vr and moves parallel to the banks. Will's route needs to be perpendicular to the banks, so that he ends up at his intended destination.

(a) In what direction should he swim relative to his intended path and

(b) if the river's width is dr, how long will it take to cross the river. Answers to (a) and (b) should be in terms of vr, vw, and dr (as necessary).