An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. One plane is 225 miles from the point and is moving at 450 miles per hour. The other plane is 300 miles from the point and has a speed of 600 miles per hour." "a. At what rate is the distance between the planes decreasing? b. If the controller does not intervene, how close will the planes come to each other?"
I understand that we can use implicit differentiation to solve part a, which shows that the difference is decreasing at 750 mph. However, I wonder why in part b, the answer is 30 minutes. In other words, the difference between the two planes (the hypotenuse of their right angle) is decreasing at a constant rate. Why is that so?