an air traffic controller is tracking two planes. to start, plane A is at an altitude of 5000 feet and plane B is at an altitude of 4467 feet. Plane A is gaining altitude at 40.5 feet per second and plane B is gaining altitude at 50.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitude be when they're at the same altitude?

Step-by-step explanation:

Answer:

52 seconds

7106 feets

Step-by-step explanation:

plane A is at an altitude of 5000 feet.

Plane A is gaining altitude at 40.5 feet per second.

Let t = the time that plane A travels before it attains same altitude with plane B.

Distance = speed * time

Distance travelled in t seconds will be

40.5 * t = 40.5t

Total distance travelled by plane A will be

5000 + 40.5t

plane B is at an altitude of 4467 feet.

Plane A is gaining altitude at 50.75 feet per second.

Let t = the time that plane B travels before it attains same altitude with plane A.

Distance = speed * time

Distance travelled in t seconds will be

50.75 * t = 50.75t

Total distance travelled by plane A will be

4467 + 50.75t

For both planes to be at the same altitude, their total distance must be equal. Therefore,

5000 + 40.5t = 4467 + 50.75t

5000-4467 = 50.75t - 40.5t

533 = 10.25t

t = 533/10.25 = 52 seconds

It will take 52 seconds for both planes to be at the same altitude.

Altitude of plane A will be

5000 + 40.5 * 52 = 7106 feets

Altitude of plane both planes will be

7106 feets