Question

At 7:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 22510 ft. and is descending at the rate of 150 ft/min. Airplane #2 has an elevation of 11260 ft. and is climbing at the rate of 100 ft/min.(1) Let t represent the time in minutes since 7:00 am, and let E represent the elevation in feet. Write an equation for the elevation of each plane in terms of t .plane #1: E(t)= plane #2: E(t)= (2) At what time will the two airplanes have the same elevation?t= minutes after 7:00 am (3) What is the elevation at that time?E= feet

Answer 1

Okay, here we have this:

1)

Plane #1:

Considering that it says that is descending each minute 150ft we take this as an subtraction:

E(t)=22510-150t

Plane #2

Considering that it says that is climbing each minute 100ft we take this as an addition:

E(t)=11260+100t

2)

Those will have the same elevation when their E (t) are equal, so we obtain the following:

22510-150t=11260+100t

-250t=-11250

t=45

t=45 minutes after 7:00 am

3)

Now, let's find the elevation at 45 minutes after 7:00 am

E(t)=22510-150t

E(45)=22510-150(45)

=22510-6750

=15760

Finally we obtain that the elevation is 15760 feet.