SOLUTION: This one if tough! I have been using the distance = rate * time but I can not figure this one, please help! A plane flies 720 mi against a steady 30-mi/h headwind and then returns

Algebra ->  Expressions-with-variables -> SOLUTION: This one if tough! I have been using the distance = rate * time but I can not figure this one, please help! A plane flies 720 mi against a steady 30-mi/h headwind and then returns      Log On


   

Question 110592: This one if tough! I have been using the distance = rate * time but I can not figure this one, please help!
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?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
in this case, time=distance/rate ... let x="speed in still air"

(720/(x+30))+(720/(x-30))=10 ... 720(x-30)+720(x+30)=10(x^2-900) ... 1440x=10(x^2-900)

x^2-144x-900=0 ... (x-150)(x+6)=0