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Two runners started simultaneously from the same point. First, they ran along the street to the stadium, and then to the finish line - three laps around the stadium. Both ran the entire distance at constant speeds, and during the race, the first runner overtook the second runner twice. Prove that the first runner ran at least twice as fast as the second.
| The first could overtake the second only on the circular track of the stadium. Since he ran onto the stadium first, he could not overtake the second on his first lap. Therefore, the overtakes must have happened when the first was running his second and third laps. While the first was running these two laps, he overtook the second by at least one lap. Consequently, the second ran no more than one lap during this time, which leads to the required statement.