A puzzle by S. Sefibekov:
Winnie-the-Pooh and Piglet set out to visit one another. They leave their houses at the same time and walk along the same road. But Piglet is absorbed in counting the birds overhead, and Winnie-the-Pooh is composing a new “hum,” so they pass one another without noticing. One minute after the meeting, Winnie-the-Pooh is at Piglet’s house, and 4 minutes after the meeting Piglet is at Winnie-the-Pooh’s. How long has each of them walked?
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Call Winnie-the-Pooh’s house W and Piglet’s house P, and call their meeting point M. Suppose it took x minutes for the two of them to travel from their starting points to M. Then Winnie-the-Pooh spent x minutes walking from W to M and 1 minute from M to P; hence WM/MP = x. And the same reasoning for Piglet gives PM/MW = x/4. Now, WM/MP x PM/MW = 1, so 1 = x2/4, and x = 2. Winnie-the-Pooh has walked for 3 minutes and Piglet for 6 minutes.
From the Russian science magazine Kvant.
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