An air traffic controller spots two airplanes at the same altitude converging to

Question

An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 120 miles from the point and has a speed of 240 miles per hour. The other is 160 miles from the point and has a speed of 320 miles per hour. SHOW WORK

(a) At what rate is the distance between the planes changing?

________________mph

(b) How much time does the controller have to get one of the airplanes on a different flight path?

_____________________min

Explanation / Answer

A) Now this is dealing with right triangles. Knowing this we can jot down a lot of information.

x = 120
dx/dt =240

y = 160
dy/dt = 320

Now before we start anything we need z. The question is asking us to find dz/dt. So let's use pythagorean's theorem.

x

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