The following problem from *Five Hundred Mathematical Challenges* was a challenge indeed, even though it appeared to be a standard travel puzzle.

“**Problem 118**. Andy leaves at noon and drives at constant speed back and forth from town A to town B. Bob also leaves at noon, driving at 40 km per hour back and forth from town B to town A on the same highway as Andy. Andy arrives at town B twenty minutes after first passing Bob, whereas Bob arrives at town A forty-five minutes after first passing Andy. At what time do Any and Bob pass each other for the nth time?”

See the Perpetual Meetings Problem