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Ant on a rubber band

Let's assume we have a rubber band that can stretch infinitely. At t = 0 s its length is 1 m and every second it's one meter longer. Now, there's an ant at one end of the rubber band. It starts to walk towards the other end (on solid ground, ant can walk at the speed of v = 0.1 m/s). Does the ant reach the other end? If so, how long does it take? How does the ant's speed change the situation?