Help with word problem needed.

Consider a thin and infinitely stretchable rubber rope held taut along an x-axis with a starting-point marked at x = 0 and a target-point marked at x = c, c > 0.

At time t = 0 the rope starts to stretch uniformly and smoothly in such a way that the starting-point remains stationary at x = 0 while the target-point moves away from the starting-point with constant speed v > 0.

A small ant leaves the starting-point at time t = 0 and walks steadily and smoothly along the rope towards the target-point at a constant speed α > 0 relative to the point on the rope where the ant is at each moment.

Will the ant reach the target-point?

Thanks a lot in advance