Question

an air traffic controller is tracking two planes. to start, plane a is at an altitude of 3788 feet and plane b is at an altitude of 5000 feet. plane a is gaining altitude at 55.5 feet per second and plane b is gaining altitude at 30.25 feet per second. how many seconds will pass before the planes are at the same altitude? seconds what will their altitude be when theyre at the same altitude? feet

Explanation:

Step1: Set up altitude equations

Let \( t \) be the time in seconds. The altitude of Plane A is \( 3788 + 55.5t \) and the altitude of Plane B is \( 5000 + 30.25t \). When they are at the same altitude, \( 3788 + 55.5t = 5000 + 30.25t \).

Step2: Solve for \( t \)

Subtract \( 30.25t \) and \( 3788 \) from both sides:
\( 55.5t - 30.25t = 5000 - 3788 \)
\( 25.25t = 1212 \)
Divide both sides by \( 25.25 \):
\( t = \frac{1212}{25.25} = 48 \)

Step3: Find the altitude

Substitute \( t = 48 \) into Plane A’s altitude formula:
\( 3788 + 55.5(48) = 3788 + 2664 = 6452 \)

Answer:

48 seconds
6452 feet