30 Apr '08 06:303 edits

Al, Ben, Carl, and Dan need to get to the special place. They are currently 20 miles from the special place, and they can each walk at a constant 4 miles per hour. They figure they can get there in 5 hours, but it would behoove them to get there as soon as possible.

Just then, they meet a friendly motorcyclist named Ed who can travel at 56 miles per hour, but can only carry one passenger with him (neither of the other four have a motorcycle license, so only Ed can drive). They make the following arrangement:

Ed will take Al on his motorcycle a certain distance (call it

The four depart as soon as the arrangements are made, and they begin from exactly 20 miles away. Assuming all turns, pick-ups, drop-offs, and accelerations to either 4 or 56 mph are instantaneous, how long will it take for the five of them reach the special place, and what was the initial distance

Just then, they meet a friendly motorcyclist named Ed who can travel at 56 miles per hour, but can only carry one passenger with him (neither of the other four have a motorcycle license, so only Ed can drive). They make the following arrangement:

Ed will take Al on his motorcycle a certain distance (call it

*x*miles) while Ben, Carl, and Dan are walking. Then Ed will immediately turn around to pick up Ben. Al will walk the rest of the journey. Ed will carry Ben until they reach Al, drop off Ben (who then continues walking with Al), and immediately turn again to get Carl (who, along with Dan, was walking the whole time). After dropping off Carl to where Al and Ben would be, Ed would go back and get Dan (again, Dan was walking the entire time). In order to minimize the time taken, Ed and Dan would reach the special place at exactly the same time as Al, Ben, and Carl.The four depart as soon as the arrangements are made, and they begin from exactly 20 miles away. Assuming all turns, pick-ups, drop-offs, and accelerations to either 4 or 56 mph are instantaneous, how long will it take for the five of them reach the special place, and what was the initial distance

*x*?