Question

26 points - Help, if you can: An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3,500 feet and Plane B is at an altitude of 2,601 feet. Plane A is gaining altitude at 40.25 feet per second and Plane B is gaining altitude at 55.75 feet per second. 1. How many seconds will pass before the planes are at the same altitude? 2. What will their altitude when they're at the same altitude?

Answer 1

1. 58 seconds

2. 5834.5 feet

Explanation:

The equation
`A(t) = 40.25t + 3500` can be used to represent the height of plane A at time t seconds. Similarly, the equation
`B(t) = 55.75t + 2601` represents the height of plane B after t seconds. To solve for when the planes are at the same height, we can set these two equations equal to get
`40.25t + 3500 = 55.75t + 2601 \Rightarrow 15.5t = 899 \Rightarrow t = 58.` So,
`\boxed{\boxed {58}}` seconds will pass before the planes are at the same altitude. Plugging in t=58 into either of the equations, we see their altitudes will be
`\boxed{\text{5834.5 feet}}` .