Question

An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 432 meters, and Plane B was just taking off. Plane A is gaining altitude at 16 meters per second, and Plane B is gaining altitude at 25 meters per second.
Let x be the number of seconds that have passed.

Altitude of plane A (in meters) =
Altitude of plane B (in meters) =

also, Write an equation to show when the two planes would be at the same altitude.

Answer 1

Answers:

The altitude expressions needed are

• plane A = 16x+432
• plane B = 25x

The planes are at the same altitude for the equation 25x = 16x+432

That equation solves to x = 48

The altitude of each plane at this point in time is 1200 feet

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Further Explanation:

x = number of seconds

Plane A starts off at 432 meters off the ground. Then we add on another 16x meters to represent it gains altitude at 16 meters per second. So that's how I got the 16x+432 for plane A's altitude.

Plane B's altitude is 25x for similar reasoning. It starts off on the ground, so the y intercept is 0.

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We set the two altitude expressions equal to one another and solve for x to find out when the planes are at the same height.

plane B = plane A

25x = 16x+432

25x-16x = 432

9x = 432

x = 432/9

x = 48

The two planes are at the same altitude at exactly 48 seconds.

• plane A altitude = 16x+432 = 16*48+432 = 1200
• plane B altitude = 25x = 25*48 = 1200

Both planes are at an altitude of 1200 feet at this time point.