SOLUTION: I need help with this problem. 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 th

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Question 96041This question is from textbook Beginning Algebra
: I need help with this problem.
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?
Here is what I know: If r is the rate of the plane (in miles per hour)in still air, then the rate against the wind would be r - 30 and the rate with the wind would be r + 30. I don't know what to do after this point. This question is from textbook Beginning Algebra

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
720/(X-30)+720/(X+30)=10
[720(X+30)+720(X-30)]/(X-30)(X+30)=10
(720X+21600+720X-21600)/X^2-900=10 NOW CROSS MULTIPLY:
10X^2-9000=1440X
10X^2-1440X-9000=0 FACTOUT THE 10
10(X^2-144X-900)=0
(X-150)(X+6)=0
X-150=0
X=150 MPH IS THE SPEED FO THE AIRPLANE IN STILL AIR.
PROOF
720/(150-30)+720/(150+30)=10
720/120+720/180=10
6+4=10
10=10