Using linear functions, it is found that the two planes will be at the same altitude in 7 minutes.
What is a linear function?
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
For the first plane:
- Initial altitude of 1000 meters, hence [tex]b = 1000[/tex].
- Ascending t a rate of 400 meters per minute, hence [tex]m = 400[/tex].
Hence, the equation is:
[tex]y_1(x) = 400x + 1000[/tex]
For the second plane:
- Initial altitude of 5900 meters, hence [tex]b = 5900[/tex].
- Descending t a rate of 300 meters per minute, hence [tex]m = -300[/tex].
Hence, the equation is:
[tex]y_2(x) = -300x + 5900[/tex]
They will be at the same altitude at the value of x for which:
[tex]y_1(x) = y_2(x)[/tex]
Hence:
[tex]400x + 1000 = -300x + 5900[/tex]
[tex]700x = 4900[/tex]
[tex]x = \frac{4900}{700}[/tex]
[tex]x = 7[/tex]
The two planes will be at the same altitude in 7 minutes.
To learn more about linear functions, you can take a look at brainly.com/question/25823744
