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?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 44686: 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?
Thank You!!!
Found 2 solutions by checkley71, stanbon:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
2*720/10=1440/10 OR 144 MPH IS THE SPEED OF THE PLANE.
SPEED WITH THE WIND WAS 144-30=114 AND THE RETURN SPEED WAS 144+30=174

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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?
With the wind DATA:
distance=720 mi;rate=plane speed + 30mph; time=d/r=720/(p+30)
Against the wind DATA:
distance=720 mi; rate=plane speed -30 mph; time=720/(p-30)
EQUATION:
time with + time against = 10 hr.
720/(p+30) + 720/(p-30) = 10
Divide thru by 10 to get:
72/(p+30) + 72/(p-30)=1
LCM=p^2-900
Multiply thru by the LCM to get:
72(p-30) + 72(p+30)=p^2-900
72p-72*30+72p+72*30=p^2-900
144p=p^2-900
p^2-144p-900=0
(p+6)(p-150)=0
p=-8 or p=150
plane speed in still air = 150 mph is the only reasonable answer.
Cheers,
Stan H.