[pdurrant]

Originally Posted by omk3

Spoiler:

Yes he will.
Every time the track stretches, his position changes by an equal percent.
So in the first second, the track is stretched by 100% and becomes 200, so his position is also moved forward by 100%. On the first second he has run 10 meters but is on the 20 meter mark of the 200 meter track.
On the second second, he runs 10 meters more, so he is now on the 30 meter mark. The track stretches by 100 meters, which is 50% of 200, so his position is now on the 45 minute mark of the 300 meter track.
And so on.
The percent of the track he has covered after each second grows (as I found in excel :P) so at one time he will have covered the whole track.
Don't ask me when though

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.