So.... notice the picture below
we know when y = 140 and x = 240, r = 250
so let's use the pythagorean theorem
now... how much time does the controller have? well, say, plane "y" is going at dy/dt of 140mph, and is 70 miles away, 140 is 2*70, so it can cover those 70 miles in 1/2 hr, and when it does, it'll collide with the other,
so, the controller has that much, less than 1/2 hr
we know when y = 140 and x = 240, r = 250
so let's use the pythagorean theorem
now... how much time does the controller have? well, say, plane "y" is going at dy/dt of 140mph, and is 70 miles away, 140 is 2*70, so it can cover those 70 miles in 1/2 hr, and when it does, it'll collide with the other,
so, the controller has that much, less than 1/2 hr