Question

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. At which point in time, measured in seconds, will Plane A and Plane B have the same altitude?

A) 12 seconds
B) 10 seconds
C) 20 seconds
D) 15 seconds

Answer 1

Upon setting up the equation for the same altitude for Plane A and Plane B and solving for x, the result obtained is 42 seconds, which does not match any of the provided multiple-choice answers, suggesting an issue with the calculation or the understanding of the question.

Step-by-step explanation:

To determine when Plane A and Plane B will have the same altitude, we set up an equation where the altitude of Plane A after x seconds plus its starting altitude equals the altitude of Plane B after x seconds plus its starting altitude.

Altitude of Plane A = 500 + 12x
Altitude of Plane B = 164 + 20x

Set the altitudes equal to each other and solve for x:

500 + 12x = 164 + 20x
20x - 12x = 500 - 164
8x = 336
x = 42

However, the answer of 42 seconds is not one of the provided choices, implying there may have been a miscalculation or a misunderstanding of the question. Double-checking the work or seeking clarification of the question is advisable.