[pdurrant]

Originally Posted by HarryT

Spoiler:

As long as the track stretches taking Achilles with it then it's clear that he will finish the race. Let us suppose that he is x% along the track when it stretches. He is still x% along it after the stretch, and every step he takes will increase "x", stretch or no stretch. The fact that the stretch is arithmetic rather than geometric ensures that he will complete the race in a finite time (which I'm afraid I can't be bothered to work out).

The right answer, but I'm not convinced that you've properly shown thar it actually is the right answer.

Spoiler:

For instance, if, instead of extending it 100m, would Achilles finish if they extended it by 100m, 200m, 300m, etc,? After all, he'll still be increasing the percentage of the track he's covered all the time.