Challenges M 217: Bike sharing, Quantum (Nov./Dec. 1997) 26, 48
Bike sharing: Town A is 30 miles from town B. Three friends want to
travel from A to B. They have two bicycles with them: one is a racing
bike, which any of them can ride at a speed of 30 mph; the other is a
mountain bike, which they ride at a speed of 20 mph. Each of them walks
at the rate of 6 mph.
Any of the friends can leave a bicycle at the side of the road, where
it will lie undisturbed until another friend comes and uses it. The
three friends want to minimize the time they spend on their journey
(we'll say that the trip is over when the last friend arrives at B).
Find the shortest possible time for this joint trip.
References:
Heinrich Hemme, Mathias Schwoerer;
Mathematischer Denkspass, Weltbild Verlag,
Augsburg, 1998, ISBN 3-89604-615-2 Problem
26: Die beiden Zechbr"uder
(two friends with one bike and two different walking speeds)