# Poor Bug, Will it ever succeed?

An extremely stretchable rubber band of natural length $$\displaystyle L$$ has its one end tied to a wall.
A bug peacefully rests at the outer end. Just when it seemed that everything was good, an evil-minded child starts pulling the outer end by a constant velocity $$\displaystyle v$$. The bug immediately realizes the danger, and simultaneously starts crawling towards the other end at a speed $$\displaystyle u$$ (relative to the band).

Will the bug ever reach the wall? If so, how long (in sec) would it take to reach it?

Answer $$\displaystyle 0$$ if you think that the bug will never reach the wall.

Details and Assumptions:
$$\bullet$$ $$\displaystyle L = 15 \text{ cm}$$
$$\bullet$$ $$\displaystyle v = 3 \text{ cm/s}$$
$$\bullet$$ $$\displaystyle u = 1 \text{ cm/s}$$

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