An ant gets onto one end of a tight rope that is 1 meter long. The ant is traveling at 1 centimeter per second, but the entire rope is being stretched an extra 1 meter a second (it can be stretched forever). Will the ant ever reach the other end of the rope?
He will reach the end of the rope eventually. Once he gets onto the rope, the rope behind him also stretches, so this must also be accounted for.