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The mouse is walking along the band, while the end of the band moves away, however the mouse is also being carried along by the expansion of the band. I think the best approach is to think in terms of the fractional coordinate of the mouse along the band, and work out its effective velocity in this coordinate.

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The elastic band could expand in both directions or either. If I assume the band expands so fast that I remain at the same point with regards to a point of reference, have I not still moved by 2m along the band after a minute? I guess it's more about the semantics of how moving along the band applies.

Also how the expansion carries the mouse has to do with its movement. E.g. if it's galloping it would not carry it.

Correct, if you structure the problem as the proportion completed at time t relative to the proportion at time t-1, then you can sum in the limit as t goes to infinity to show surprisingly that he gets to the end under both scenarios.

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