An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 1833 feet and Plane B is just taking off. Plane A is gaining altitude at 35.25 feet per second and Plane B is gaining altitude at 70.5 feet per second.

Question

How many seconds will pass before the planes are at the same altitude?

What will their altitude be when they're at the same altitude?

Answer 1

To find the number of seconds it will take for the planes to be at the same altitude, we can set up an equation:

1833 + 35.25x = 70.5x

Solving for x:

1833 = 35.25x + 70.5x
1833 = 105.75x
x = 1833/105.75
x ≈ 17.34 seconds

So it will take approximately 17.34 seconds for the planes to be at the same altitude.

Now, to find the altitude they will be at when they are at the same altitude, we can substitute x back into the equation:

1833 + 35.25(17.34) = 70.5(17.34)
1833 + 610.085 = 1222.97
2443.085 = 1222.97

Therefore, the altitude of both planes when they are at the same altitude will be approximately 2443.085 feet.

Answer 2

You sure?

Answer 3

Apologies for the mistake in my previous response. Let's correct it:

To find the number of seconds it will take for the planes to be at the same altitude, we can set up the equation:

1833 + 35.25x = 70.5x

Solving for x:

1833 = 70.5x - 35.25x
1833 = 35.25x
x = 1833 / 35.25
x ≈ 52 seconds

So it will take approximately 52 seconds for the planes to be at the same altitude.

Now, to find the altitude they will be at when they are at the same altitude, we can substitute x back into the equation:

1833 + 35.25(52) = 70.5(52)
1833 + 1836 = 3642
3669 = 3642

Therefore, the corrected altitude of both planes when they are at the same altitude will be approximately 3669 feet. Thank you for pointing out the error.