Question

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2886 feet and Plane B is just taking off. Plane A is gaining altitude at 25.25

feet per second and Plane B is gaining altitude at 80.75 feet per second.
How many seconds will pass before the planes are at the
same altitude?
seconds
What will their altitude be when they're at the same
altitude?
feet

Answer 1

It will take 52 seconds before Planes A and B are at the same altitude. They will both be at an altitude of 4203 feet when they reach the same level.

Step-by-step explanation:

To determine when two planes will be at the same altitude, we can set up an equation where the altitude of Plane A plus its altitude gain per second times the number of seconds equals the altitude gain per second of Plane B times the number of seconds, since Plane B starts at ground level (0 feet).

Let t be the number of seconds. The equation would then be:

Altitude of Plane A + (Rate of climb of Plane A × t) = (Rate of climb of Plane B × t)

2886 + 25.25t = 80.75t

To find t, we can rearrange the equation:

80.75t - 25.25t = 2886

55.5t = 2886

t = 2886 / 55.5

t = 52 seconds

Now that we know the number of seconds, we can determine their altitude:

Altitude of Plane A or Plane B = Rate of climb of Plane B × t

Altitude = 80.75 × 52 = 4203 feet

Therefore, it will be 52 seconds before the planes are at the same altitude, and they will be at an altitude of 4203 feet when they're at the same altitude.