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Saturday, July 26, 2008

Cork in the Canal

A swimmer jumps from a bridge over a canal and swims 1 kilometer stream up. After that first kilometer, he passes a floating cork. He continues swimming for half an hour and then turns around and swims back to the bridge. The swimmer and the cork arrive at the bridge at the same time. The swimmer has been swimming with constant effort.

The Question: How fast does the water in the canal flow?

Answer: If you have written down a full paper of mathematical formulas, you have been thinking too complicated...
It is obvious that the cork does not move relatively to the water (i.e. has the same speed as the water). So if the swimmer is swimming away from the cork for half an hour (up stream), it will take him another half hour to swim back to the cork again. Because the swimmer is swimming with constant effort, his speed is constant relatively to the speed of the water. You can look at it as if the water in the river doesn't move, the cork doesn't move, and the swimmer swims a certain time away from the cork and then back. So in that one hour time, the cork has floated from 1 kilometer up stream to the bridge.

Conclusion: The water in the canal flows at a speed of 1 km/h.

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