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a cockroach is trapped in a trash compactor whose walls are 100 meters apart. Thr walls of the compactor begin to close in on the cockroach at a speed of 1 meter per hour. Sensing doom, the cockroach panics and runs from one of the walls that is closing in to the opposite wall, over and over and over until eventually, squish. The cockroach runs at a speed fo 20 meters per hour, and starts at one of the walls. how much distance does the cockroach run before he does? assume that r2-d2 does not care about cockroaches.

I feel like this is simple algebra?

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    Please, try to make the title of your question more informative. E.g., *Why does a imply a+c?* is much more useful for other users than *A question about inequality.* From [How can I ask a good question?](http://meta.math.stackexchange.com/a/589/): *Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader.*2012-11-26

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Hints:

(1) How much time $\,t\,$ does it take the walls to close?

(2) how much distance does the roach run in time $\,t\,$?

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I am assuming each wall moves $\frac 12$ meter/hour for a total of $1$ meter/hour.

You can do it by summing the series. Calculate the cockroach runs before the first reversal, then the second, etc.

You can also reason that it will take 100 hours for the walls to come together and the cockroach runs 20 meters/hour

There is a famous legend about Von Neumann: search for fly puzzle.