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## Homework Statement

"You have a 1 km long rubber band with one end attached to the wall, and the other in your hand. The bug begins to crawl towards you on the rubber band, starting from the wall, at a rate of 1 cm/sec. As he crawls the first centimeter you extend the rubber band 1 km; when he crawls the second centimeter you extend the rubber band another 1 km, and so on, every second. The question is: Does the bug ever reach you, and if so, in how much time?"

## Homework Equations

[itex]L=1km[/itex]

[itex]v=1km/s[/itex]

[itex]u=1 cm/s[/itex]

x = distance between the bug and the wall

## The Attempt at a Solution

I came up with the following equation:

[itex]dx=(u+\frac{x}{L+vt})dt[/itex]

but I don't know how to solve it. I'm thinking of integrating it from [itex]0[/itex] to [itex]T[/itex] and then setting it equal to [itex]L+vT[/itex] and then solving for [itex]T[/itex] but I don't know how to do this (I don't have experience with differential equations)

Is it possible to get a value for [itex]T[/itex] with this equation, and if so, how would I do it?

Thanks.

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