Marc P. answered • 11/10/19

Ivy League Grad to Help with Standardized Tests and Academic Work

The actual rate of travel is the plane's rate plus the wind rate (positive if helping the plane, negative if hindering the plane). We'll need to use equation D = RT, but we'll need to use it twice since the plane makes two trips. Let's call the plane's rate p and the wind's rate w.

For the first trip, we have:

D = RT

1080 = (p + w)*6

For the second trip, we have:

D = RT

(2/3)*1080 = (p - w)*6

Now we have two equations and two variables (p and w), so we should be able to solve for each variable. We can expand the two equations to get:

1080 = 6p + 6w

720 = 6p - 6w

Now we can solve this system of equations using the elimination method. First, add the two equations together to eliminate the w variable. That will give you a single equation with one variable (p), which you can solve for p. Next, subtract the bottom equation from the top one to eliminate the p variable. That will give you a single equation with one variable (w), which you can solve for w. I think that you can do that, but let me know if you have any trouble with the algebra.