Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 425 knots (nautical miles per hour; a nautical mile is 2000 yd or 6000 ft.) Plane B is approaching the intersection at 443 knots. At what rate is the distance between the planes decreasing when Plane A is 5 nautical miles from the intersection point and Plane B is 8 nautical miles from the intersection point?

Question

Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 425 knots (nautical miles per hour; a nautical mile is 2000 yd or 6000 ft.) Plane B is approaching the intersection at 443 knots.   At what rate is the distance between the planes decreasing when Plane A is 5 nautical miles from the intersection point and Plane B is 8 nautical miles from the intersection point?