This was passed to me haphazardly, so I apologize in advance for any mistakes.
You are on a circular lake in a boat. There is a monster at the edge of the lake, waiting to eat you, who can't go in the water. You must reach shore before he reaches you there; then you are safe, regardless of how close he is to you. You can row at speed x, but he can run at speed 4x. What do you do?
NB: assume the monster pursues its optimal strategy, which is to move always to the point on shore to which you are closest.
EDIT: https://puzzling.stackexchange.com/questions/2155/the-lake-monster