Thread: 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

You can take this exactly as two cars starting from rest, one at at x = 0 and another at x = c. The cars go at speed v and α respectively towards the positive x direction.

By logic, you will deduce that if α > v, the cars will eventually meet.
If , the cars will never meet.

But this problem is given in a book of ODEs(Ordinary Differential Equations).......I have to solve this problem using some kind of a differential equation , not logic.....