Hans and Franz are two fitness fanatics. On a run from A to B, Hans runs half the way and walks the other half. Franz runs for half the time and walks for the other half. They both run at the same speed and walk at the same speed. who finishes first?

Answer : Hans

Here is an informal argument. Since Franz and Hans run

faster than they walk, Hans will go farther in the time that he runs

than in the equal time that he walks. Therefore he covers more

distance at a run than Franz does, since Fred covers equal distances

running and walking.

While both are walking or both are running, they will cover equal

distances. Therefore subtract this distance from the total distance.

The remaining distance is covered by Franz at a walk and by Hans at a

run, so Hans will finish first.