An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2093 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 75.75 feet per second.How many seconds will pass before the planes are at the same altitude?secondsWhat will their altitude be when they're at the same altitude?feet
Question
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2093 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 75.75 feet per second.How many seconds will pass before the planes are at the same altitude?secondsWhat will their altitude be when they're at the same altitude?feet
Solution
To solve this problem, we need to set up an equation where the altitudes of Plane A and Plane B are equal.
We know that Plane A starts at 2093 feet and is gaining altitude at a rate of 30.25 feet per second. So, the altitude of Plane A at any given time (t) can be represented as:
Altitude of Plane A = 2093 + 30.25t
Plane B is just taking off, so it starts at 0 feet and is gaining altitude at a rate of 75.75 feet per second. So, the altitude of Plane B at any given time (t) can be represented as:
Altitude of Plane B = 75.75t
We set these two equations equal to each other to find the time when the planes are at the same altitude:
2093 + 30.25t = 75.75t
Subtract 30.25t from both sides to isolate the variable on one side:
2093 = 45.5t
Then, divide both sides by 45.5 to solve for t:
t = 2093 / 45.5 ≈ 46 seconds
So, it will take approximately 46 seconds for the planes to be at the same altitude.
To find the altitude at which they will be at the same height, we can substitute t = 46 into either of the original equations. Using Plane B's equation:
Altitude = 75.75 * 46 ≈ 3484.5 feet
So, the planes will be at the same altitude of approximately 3484.5 feet after 46 seconds.
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