Question

A plane travels from Orlando to Denver and back again. On the five-hour trip from Orlando to Denver, the plane has a tailwind of 40 miles per hour. On the return trip from Denver to Orlando, the plane faces a headwind of 40 miles per hour. This trip takes six hours. What is the speed of the airplane in still air? (2 points)

all i need is to know where to place the variables but more is welcome

Answer 1

This is a systems of equations problem that involves d = rt

Answer 2

except r=a ± w

Answer 3

So what you'll have is a two-system general form where:

d = (a + w)t
d = (a - w)t

Answer 4

You input the given information then solve the system. When you input the information and arrange both the equations to their appropriate form, then you should be able to solve the system

Answer 5

By the way

a = the speed of the plane
w = the speed of the wind

Answer 6

To Denver from Orlando, it takes 5 hr
To Orlando from Denver, it takes 6hr
The headwind and tail wind are both 40, so inputting everything you get:

d = 5(a + 40)
d = 6(a - 40)

Answer 7

Now you have a solvable two variable system:

d = 5a + 200
d = 6a - 240

Answer 8

This is the same as if you had a system of equations

y = 5x + 200
y = 6x - 240

Answer 9

This should be familiar to you.

Answer 10

Anyway, we'll solve for a:

d = 5a + 200
d = 6a - 240

What we'll do is eliminate the d variable. So subtracting the first equation from the second we get:

0 = a -440

Add 440 to both sides:

440 = a

Thus the speed of the plane is 440mph

Answer 11

Any questions?