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 150 miles from the point and has a speed of 900 miles per hour. The other is 200 miles from the point and has a speed of 1200 miles per hour. (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?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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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 150 miles from the point and has a speed of 900 miles per hour. The other is 200 miles from the point and has a speed of 1200 miles per hour.

(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?
h
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