Question

Two drones are descending from the sky in vertical lines. A black drone is currently at an altitude of 1,170 feet and is dropping at a rate of 64 feet per minute. A white drone is at an altitude of 966 feet and is dropping at a rate of 52 feet per minute. How many minutes will it take for the two drones be at the same altitude? Use the variable n to represent the unknown quantity.

Answer 1

It will take 17 minutes for the two drones to reach the same altitude. We set up an equation for each drone's altitude after n minutes, equalized them, and solved for n.

Step-by-step explanation:

To determine how many minutes it will take for the two drones to be at the same altitude, we need to set up an equation that represents the altitude of each drone after n minutes.

The black drone starts at 1,170 feet and descends at a rate of 64 feet per minute. Therefore, its altitude after n minutes is 1,170 - 64n feet.

The white drone starts at 966 feet and descends at a rate of 52 feet per minute. So, its altitude after n minutes is 966 - 52n feet.

For them to be at the same altitude, these two expressions need to be equal:

1,170 - 64n = 966 - 52n

Now, we solve for n to find the number of minutes it will take:

1,170 - 966 = 64n - 52n

204 = 12n

n = 204 / 12

n = 17

It will take 17 minutes for the two drones to be at the same altitude.