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.
While Piglet is absorbed in counting the birds overhead 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?
Source: Russian science magazine Kvant
Let the distance between their houses be D, and the time (in minutes) when they meet be T.
Winnie's speed is thus D/(T+1), and the distance he's traveled in T minutes (i.e. when they pass each other) is DT/(T+1)
Similarly, Piglet's speed is D/(T+4) and the distance he's traveled in T minutes is DT/(T+4).
The sum of these two distances must equal the total distance between their houses, so we have DT/(T+1) + DT/(T+4) = D.
Simplifying that gives us T^2 - 4 = 0, so T = 2. Therefore, Winnie walks for a total of 3 minutes and Piglet walks for a total of 6 minutes.
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Posted by tomarken
on 2016-05-05 08:34:52 |
Solution
