Question 41867
In problems like this, we always use distance = rate * time, or D = RT.
Thus T = D/R.  Let R be the plane's speed in still air.
Going against the wind, we have
T1 = 720 / (R - 30) and
T2 = 720 / (R + 30)
But these two times add to 10 hours, so we have
720 / (R - 30) + 720 / (R + 30) = 10
Now multiply everything by (R+30)(R-30) to clear fractions...
720(R+30) + 720(R-30) = 10(R+30)(R-30)
Now solve for R...
720R + 21600 + 720R - 21600 = 10(R^2 - 900)
1440R = 10(R^2 - 900)
144R = R^2 - 900
R^2 - 144R - 900 = 0
(R - 150)(R + 6) = 0
R = 150 mph