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Hi. Problem driving me crazy. Please help. Two airplanes (at the same height) are flying away from an airport at a right angle to each other. Plane Y is 190 miles from the airport, the distance between them is 500 mi, plane Y is traveling at a speed of 490 mi/hr, and the distance between them is increasing by 440 mi/hr. How fast is plan X traveling (Do not assume the planes departed at the same time.) Answer in mi/hr.
They are at right angles.
The side with Y is 190 mi.
The hypoteneuse is 500 mi.
The other sides is √(500² - 190²) = √(250,000 - 36,100) = X.
We know that X² + Y² = D² where D is the diagonal between them.
Differentiating gives you 2XdX + 2YdY = 2DdD.
I found X above, Y is 190, dY was given as 490,
D is given as 500, and dD 440.
Put all of these into the equation and
the value of dX can be found by simple algebra.
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