Two airplanes are flying in the air at the same height. Airplane A is flying east at 300mi/h and airplane B is flying north at 200mi/h. If they are both heading to the same airport, located 90 miles east of airplane A and 120 miles north of airplane B, at what rate is the distance between the airplanes changing

Step-by-step explanation:

The change of distance over time of the plain A is 300 mi/hour and 200 mi/hour for plane B. O is the point of the airport.

So, the distance from A to O AO = 90 miles and BO = 120 miles.

Now, we have a right triangle here.  We can use the Pythagorean theorem, so the distance between the planes will be:

(1)

If we take the derivative of the equation (1) we could find the change of the distance between planes.

Finally,

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step-by-step explanation: