An air traffic controller is tracking two planes. to start, plan a is at an altitude of 2172 feet and plan b is just taking off. plan a is gaining altitude at 35.25 feet per second and plan b is gainnig altitude at 80.5 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:

Plane A is already at an altitude of 2172 feet.

Let this be called the "initial altitude" of plane A and be represented by  feet

Likewise, the initial altitude of Plane B will be zero, because the plane B has just taken off from ground.

Thus,  

It is given that the altitude gaining speed of plane A is 35.25 feet/second.

Also, it is given that the altitude gaining speed of plane B is 80.5 feet/second.

Now, if at some point in time both the planes are at the same altitude, then obviously, the same amount of time, , must have passed for both the planes.

Thus, altitude of plane A after those  seconds will be:

(Equation 1)

Likewise, the altitude of plane B after those  seconds will be:

(Equation 2)

We know that after  seconds, the altitude will be the same. Thus, our guiding equation will be:

Which can be simplified to:

Thus, 48 seconds will pass before the planes are at the same altitude.

The altitude of the planes when they are at the same altitude can be calculated by putting  in any of the two equations, (Equation 1) or (Equation 2).

Thus Altitude of the planes when they are at the same altitude, by using (Equation 1) is:

feet

where is the rest of the

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