Problem #96 from Mathproblems.info (at http://mathproblems.info/group5.html) was one I have seen before as a kid :
“Three people (A, B, and C) need to cross a bridge. A can cross the bridge in 10 minutes, B can cross in 5 minutes, and C can cross in 2 minutes. There is also a bicycle available and any person can cross the bridge in 1 minute with the bicycle. What is the shortest time that all men can get across the bridge? Each man travels at his own constant rate.”
When I saw this problem as a kid there was the caveat that only one person could cross the bridge at any one time. For that case the fastest solution is to have
(1) A crosses with the bicycle. (2) C crosses. (3) C crosses back with the bicycle. (4) B crosses with the bicycle. (5) C crosses. This makes for a total crossing time of (1+2+1+1+2) or 7 mins.
The two new twist that the Mathproblems.info guys put on the problem was to remove the restriction that only one person could cross at a time, and allowing the bike to be left anywhere on the bridge. I am still working on this new version of the problem.