The duck and the fox

[I got this problem from Koen Claessen.]

A duck is in circular pond. The duck wants to swim ashore, because it wants to fly off and this particular duck is not able to start flying from the water. There is also a fox, on the shore. The fox wants to eat the duck, but this particular fox cannot swim, so it can only hope to catch the duck when the duck reaches the shore. The fox can run 4 times faster than the duck can swim. Is there always a way for the duck to escape?

March 2009

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