That Brainteaser from A Beautiful Mind

Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time, a fly that travels at a steady 15 m.p.h. starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels.

Question: what total distance did the fly cover? (Highlight below for answer)

If you are trying to solve this using calculus or differential equations, you are wasting time. The two bicycles start 20 miles apart, each going the same speed, so each bicycle must travel 10 miles before meeting the other bicycle. Since they are each traveling at a rate of 10 m.p.h., this will take 1 hr. In the meantime, the fly will zoom back and forth at 15 m.p.h., for one hour. So, he will cover a total distance of 15 miles.