SOLUTION: Two airplanes leave from an airport at the same time. One travels due south at a speed of 420 miles per hour, and the other travels due west at a speed of 560 miles per hou

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Question 1131513: Two airplanes leave from an airport at the same time. One travels due south at a speed of
420
miles per hour, and the other travels due west at a speed of
560
miles per hour. How long until the distance between the two airplanes is
3150
miles?
Answer by greenestamps(13206)   (Show Source): You can put this solution on YOUR website!


Due south and due west are paths that are perpendicular to each other, so a triangle showing the planes' paths and the distance between the planes is a right angle.

Observe that the two speeds are 420 = 140*3 mph and 560 = 140*4 mph. So the right triangle is a scale model of the 3-4-5 right triangle; the distance between the planes is increasing at a rate of 140*5 = 700 mph.

The number of hours required for the distance between the planes to be 3150 miles is



ANSWER: It will take 4.5 hours for the distance between the planes to be 3150 miles.
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