SOLUTION: A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in still air? T

Question 41867This question is from textbook
: A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in still air?
Thanks! This question is from textbook

Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
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
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