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I found this « Worm on the rubber band » problem in Concrete Mathematics book.

A slow worm $W$ starts at one end of a meter-long rubber band and crawls one centimetre per minute toward the other end.

At the end of each minute, a keeper of the band $K$ stretches it one meter.

Does the worm ever reach the finish?

The given solution is: $W$ reaches the finish if and when $H(n)$ ever surpasses 100, where $H(n)$ is the $n$th Harmonic number.

How to solve this generalized problem with continuous data and with $W$ crawling with a velocity $u=f(t)$ and $K$ crawling with velocity $v=g(t)$ where $u(t)$ and $v(t)$ are both arbitrary functions of time.

For example, I want to find if and when the worm will reach the end of a rubber band of length $L$ if (with $a$ and $b$ constants) $u(t)=a*t$ and $v(t)=b*(t)$ ?

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    You should express the function $h(t)$ that tells you the relative position on the rubber band.2011-05-21

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