A Russian problem from the 1999 Mathematical Olympiad:
A father wants to take his two sons to visit their grandmother, who lives 33 kilometers away. His motorcycle will cover 25 kilometers per hour if he rides alone, but the speed drops to 20 kph if he carries one passenger, and he cannot carry two. Each brother walks at 5 kph. Can the three of them reach grandmother’s house in 3 hours?
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Yes. The father sets out with his first son, leaving the second boy to walk alone. Father and son drive 24 kilometers, which takes 6/5 hours. Then the father puts down the first son and rides back to meet the second son 9 kilometers from home, which takes 3/5 hours. Finally he and the second son ride 6/5 hours more and reach grandmother’s house just as the first son is arriving there on foot. Each son spends 6/5 hours riding 24 kilometers and 9/5 hours walking 9 kilometers, so the three of them reach grandmother’s in exactly 3 hours.
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