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Originally Posted by Gatorade Frost
It seems to me like it's just a Y=X and a Y=3X linear equation? They'd never intersect except at (0,0)
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No, because it's just like the old problem about the guy that falls in a hole, climbs 2 feet and slips back 1 foot. He ends up taking less time to get out than you think because the last time he climbs 2 feet, he's out, so he won't slip back down.
Once the turtle gets to the point that, after the band is stretched, he's within 1 foot of Achilles, there won't be another stretching because the turtle will just take that last step. . .
I think the graph would be curved. And the turtle would rapidly start making more progress once he reaches the halfway mark since now most of the stretching happens behind him.