MathNet 2011 Question 48

Two runners started simultaneously from one point on the street. Each of them ran along the street to the stadium, and then three laps around the stadium. Each runner ran at a constant speed along the whole distance, and the first runner had overtaken the second runner twice. Prove that the speed of the first runner is at least twice the speed of the second one. (The starting moment is considered not to be an overtaking.)

(I. Rubanov)