Question

One plane at 520 ft. is ascending at a rate of 40 ft. per minute, while another plane at 3800 ft. is descending at a rate of 120 ft. per minute. How long will it take the 2 planes to be at the same altitude?

Answer 1

You want to write down an equation for the height of both airplanes at time t.

Call the height of the first plane a(t); the second plane b(t)

Now you know that
a(0) = 520 ft
a(1) = 520 - 40 = 480
a(2) = 520 - 80 = 440

Hence what's the equation for a(t) in general?

Answer 2

a(t) - b(t) = 3800 ?

Answer 3

you add 40 for every time you subtract. like minus 40, minus 80, and now it's going to be minus 120?

Answer 4

Forget that for moment. What will want to do is solve the equation a(t) = b(t) because that's when the planes are at the same height.

But before we get to that equation, we're going to know what a(t) and b(t) is.

So look again at the pattern for a(t) and see if you write down the general form of the equation for a(t):

And apologies ... I should have added as you say!!


a(0) = 520 ft
a(1) = 520 + 40 = 560
a(2) = 520 + 80 = 600
a(3) = 520 + 120 = 640

Answer 5

Hence a(t) = 520 + 40t
makes sense?

Answer 6

and what do i put for a(t) ? 520?

Answer 7

In general, at t minutes, the first plane is at an altitude of
a(t) = 520 + 40t

Answer 8

So at t = 0 minutes, the plane is where it began,
a(0) = 520

At t = 1 minute, it's 40 feet higher
a(1) = 520 + 40 = 560

At t = 2 minutes, it's another 40 feet higher
a(2) = 520 + 2(40) = 520 + 80 = 600

etc.

Make sense?

Answer 9

Again, the formula for a(t) is
a(t) = 520 + 40t

Answer 10

oh okay! thank you!! :)

Answer 11

Now, " another plane at 3800 ft. is descending at a rate of 120 ft. per minute. "

So what's the equation for b(t)?

Answer 12

& i have last word problem, if you have time?

Answer 13

b(0) = 3800
b(1) = 3800 - 120
b(2) = 3800 - 240
...

Answer 14

b(t) = 3800 - 120x

Answer 15

Right.

Now solve

a(t) = b(t)

Answer 16

120t *

Answer 17

okay, now i can do this part by myself:) thank you!

Answer 18

ok. I've got to go. Good luck.

Answer 19

:)