Question

10. Plane A is flying at an altitude of 5000 feet. It starts descending (going down) at a rate of 100 feet per minute. Plane B is flying at an altitude of 4100 feet. It starts ascending (going up) at a rate of 50 feet per minute. If the planes start changing altitude at the same time, how many minutes until they are flying at the same altitude?​

Answer 1

It takes 6 minutes until they are flying at the same altitude..

Since Plane A is flying at an altitude of 5000 feet. It starts descending (going down) at a rate of 100 feet per minute, in time t, it descends a distance of 100t.

So, its distance from its original altitude is d = 5000 - 100t. (negative since it is descending)

Also, Plane B is flying at an altitude of 4100 feet. It starts ascending (going up) at a rate of 50 feet per minute. In time t, it ascends a distance of 50t.

So, its distance from its original altitude is D = 4100 + 50t. (positive since it is ascending)

So, to find the time the planes are flying at the same altitude, d = D

So, 5000 - 100t = 4100 + 50t

So, 5000 - 4100 = 100t + 50t

900 = 150t

dividing through by 150, we have

t = 900/150

t = 6 minutes

So, it takes 6 minutes until they are flying at the same altitude.

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