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.
