Here is another challenging problem from the Polish Mathematical Olympiads. Its generality will cause more thought than for a simpler, specific problem.
“A cyclist sets off from point O and rides with constant velocity v along a rectilinear highway. A messenger, who is at a distance a from point O and at a distance b from the highway, wants to deliver a letter to the cyclist. What is the minimum velocity with which the messenger should run in order to attain his objective?”
See the Tired Messenger Problem