[omk3]

Originally Posted by pdurrant

You have the right answer, but you haven't actually shown that it's the right answer.

Spoiler:

Just because the percentage he's travelled always increases, that doesn't necessarily mean that he'll eventually get to the end of the track.
Consider the sequence where he always covers an extra half of the percentage he covered in the previous 10m — he'll cover 10%, 15%, 17.5%, 18.75%, .... but he'll never actually get to 20% of the track, let alone more. You need to show that with the values given in the question he will eventually get 100% of the way along the track.

Spoiler:

I found in excel (by brute force) that it will take him 12367 seconds to finish the track! The logical reason for this is, I think, that the position of the runner is increased by the same percentage as the track, *plus* 10 meters. So he is slowly but surely moving forward.