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Infinitely stretchable elastic band

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Imagine an infinitely stretchable elastic band where one end is attached to a vertical wall and the other on a horse, as shown in figure. On the elastic band, very close to the wall, there is a snail. If we assume that the initial length of the band is L, and the horse and snail start moving with constant rapideces v y u (v > u), respectively, how long time the snail reached the horse?

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