Doris and Forrest start out on a bike trip, but on the way Doris' bicycle breaks down. They agree to share the remaining bicycle. They begin simultaneously, Forrest on foot, Doris riding the good bike. After a certain distance, Doris dismounts, leaves the bicycle behind and continues on foot. When Forrest reaches the waiting bicycle, he mounts it and rides until he catches up with Doris. He then dismounts, and the process repeats until they reach their goal.
How far from their destination should the the bicycle be left behind the final time to ensure they reach their destination at precisely the same moment? The distance from the breakdown to the destination is 60 miles, and they both walk at a constant rate of 5 mph and ride at a constant rate of 15 mph.