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Old 07-13-2010, 02:18 AM   #14
pdurrant
The Grand Mouse 高貴的老鼠
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Quote:
Originally Posted by Shayne Parkinson View Post
Spoiler:

Yes, he'll get there eventually. Because the track stretches equally along its length, the percentage Achilles has covered is not changed by each stretch. After a stretch he then runs another 10 metres, increasing his percentage covered, before the track stretches again.

After one second, he's run 10m, which is 10% of the track. The track then stretches to 200m, so the son of Thetis is now at the 20m mark (10 * (200/100)), still at 10%.

After two seconds, he's at 30m, 15% of the track. The track stretches to 300m, taking Achilles to 45m (30 * (300/200)), still 15%.

After three seconds, 18.33%.

After four seconds, 20.83%.

And so on, gradually approaching 100%.
Yes, the right answer, but your reasoning is not sufficient.

Spoiler:
For instance, if, instead of extending it 100m each time, would Achilles finish if the gods 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. — 10%, 15%, 17.5%, 18.9%, 19.8%,...
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