Question

An airplane makes a 400 mile trip against a headwind in 4 hours. The return trip takes 2.5 hours, the wind now being a tailwind. If the plane maintains a constant speed with respect to still air, and the speed of the wind is also constant and does not vary, find the still-air speed of the plane and the speed of the wind.

To get anything out of this, I know I should first create a system of equations; two equations to be exact. The thing is that I don't know how to set up said equations. I can solve for variables once I have my system in play, but can not set it up.

Answer 1

@jaynater here is how you do this

Answer 2

We would be looking for the number of miles \[V_{p}= miles/h\]

Answer 3

Therefore, the internal equation would be \[V_{1}=V_{p}-V_{w}\]

Answer 4

And the secondary internal equation would be \[V_{2}=V_{p}+V_{w}\]

Answer 5

And we know that the distance 400 miles on the FIRST and SECOND are the same.

Answer 6

Hold on, I think I figured it out after staring at it for long enough, and what you're saying is kind of confirming that for me.

Answer 7

Ok

Answer 8

Let me know if your stuck

Answer 9

Let X represent the constant still-air speed of the plane, and Y the speed of the wind. Let's first take that 400/4 (400-mile trip and the initial 4 hours) is 100 mph and that 400/2.5 (400-mile trip and the second 2 hours) to get 160 mph. So, we can draw two equations out of this. Our equations should look like this:

x+y=160
x-y=100

Using elimination, we can get rid of y to achieve the still-air speed of the plane after some algebra, which comes out to 130 mph if I did it right. With this number representing the variable, we can plug it into X to solve for y. When this occurs, y should come out to a wind speed of 30 mph.

Is this correct?

Answer 10

It's correct

Answer 11

Thank you.

Answer 12

\[V_{p} = 130 miles/h\]
and
\[V_{w} = 30 miles/h\]