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 429 knots (nautical miles per hour; a nautical mile is 2000 yd or 6000 ft.) Plane B is approaching the intersection at 450 knots.

At what rate is the distance between the planes decreasing when Plane A is 3 nautical miles from the intersection point and Plane B is 3 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 429 knots (nautical miles per hour; a nautical mile is 2000 yd or 6000 ft.) Plane B is approaching the intersection at 450 knots. 

At what rate is the distance between the planes decreasing when Plane A is 3 nautical miles from the intersection point and Plane B is 3 nautical miles from the intersection point?

anonymous · Answer

|dw:1412477430448:dw|

anonymous · Answer

I got .5(-5274/sqrt(18)), but I don't think that's correct. Any idea where I may have goofed?

anonymous · Answer

$$\frac{ dd }{ dt }=\frac{ -3*429-3*450 }{ \sqrt{3^2+3^2} }=\frac{ -3\left( 429+450 \right) }{ 3\sqrt{2} }$$
$$=-\frac{ 879 }{ \sqrt{2} }=-\frac{ 879\sqrt{2} }{ 2 }miles /hr$$
negative shows it is decreasing.