An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 500 meters, and Plane B was at an altitude of 164 meters. Plane A is gaining altitude at 12 meters per second, and Plane B is gaining altitude at 20 meters per second.Let x be the number of seconds that have passed.(a)For each plane, write an expression for the altitude of the plane after x seconds.AltitudeofPlaneA(in=meters)AltitudeofPlaneB(in=meters)(b)Write an equation to show when the two planes would be at the same altitude.
(a)
- Altitude of Plane A after x seconds: 500 + 12x
- Altitude of Plane B after x seconds: 164 + 20x
(b)
To find when the two planes would be at the same altitude:
500 + 12x = 164 + 20x
Solving for x:
500 - 164 = 20x - 12x
336 = 8x
x = 42
Therefore, the two planes would be at the same altitude after 42 seconds.
Write an equation to show when the two planes would be at the same altitude.
To show when the two planes would be at the same altitude, we can set the expressions for the altitudes of the two planes equal to each other:
500 + 12x = 164 + 20x
This equation represents the point in time when Plane A is at the same altitude as Plane B.