# Ant's quest

Calculus Level 5

A flat piece of rubber, perfectly horizontal, has one end attached to a wall, while the other end is exactly $$100\text{ cm}$$ from the wall. An ant is resting on this far end.

A machine begins stretching the far end of the rubber horizontally away from the wall at a rate of $$10\text{ cm/s}$$, and the ant instantly starts crawling towards the end anchored to the wall at a rate of $$5\text{ cm/s}$$ relative to the rubber.

How long, in seconds, does it take for the ant to reach the end anchored to the wall, to one decimal place? If you think the ant will never reach the anchored end, enter $$0.0$$.


Details and Assumptions:

• The rubber does not break under the strain of being stretched, and can be stretched to an indefinite length.
• It stretches uniformly during this process.
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