@marcfbellemare you could get into catenaries and solve the height for every distance between, but the ground answer is easier

@marcfbellemare that's where the shape of the ground comes into play.

@marcfbellemare when they are adjacent, the rope folds in half to 75 feet, so you can hang it at the top and get 25 feet. When they are 150 feet you can attach it a quarter of the way up the pole. The problem also says nothing about the shape of the ground.

@marcfbellemare anywhere between zero and 150 feet apart.