Question

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2652 feet and Plane B is just taking off. Plane A is gaining altitude at 30.25 feet per second and Plane B is gaining altitude at 85.5 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?

Answer 1

To find out when the two planes will be at the same altitude and what that altitude will be, you can set up an equation based on their altitudes and rates of ascent:

Let t be the time in seconds.

- For Plane A: AltitudeA(t) = 2652 + 30.25t

- For Plane B: AltitudeB(t) = 85.5t

Now, you want to find when they are at the same altitude, so you set their altitudes equal to each other:

2652 + 30.25t = 85.5t

Now, solve for t:

2652 = 85.5t - 30.25t

2652 = 55.25t

t = 2652 / 55.25

t ≈ 48 seconds

So, it will take approximately 48 seconds for the two planes to be at the same altitude. To find their altitude at that time, you can plug this value of t back into either of the altitude equations. Let's use Plane A's equation:

AltitudeA(48) = 2652 + 30.25 * 48 = 2652 + 1452 = 4104 feet

So, when the planes are at the same altitude after about 48 seconds, their altitude will be 4104 feet.