SOLUTION: A plane flies 720 miles against a steady 30mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 hrs, what is the plane's speed in still

Question 115726:
A plane flies 720 miles against a steady 30mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 hrs, what is the plane's speed in still air?

720/30 = 10/x
720x = 30*10
720x = 300
720x/720 = 300/720
Am I on the right track on solving this problem because the answer I come up with is not a whole number?
Found 2 solutions by josmiceli, checkley71:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
s = the plane's speed in still air
w = wind speed
The problem says mi/hr
(time going) + (time returning) = total time
The problems says total time = 10 hrs
Note that distance/rate = time

multiply both sides by

solve using quadratic formula

a = 1
b = -144
c = -900

The positive answer is the only one that makes sense
The plane's speed in still air is 150 mi/hr
check answer:

OK
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
D=RT
T=D/R
10=720/(R-30)+720/(R+30) COMBINE THE FRACTIONS USING THE COMMON DENOMINATOR:
(R-30)(R+30)
10=[720(R+30)+720(R-30)]/(R-30)(R+30)
10=(720R+21600+720R-21600)/(R^2-900)
10=1440R/(R^2-900) CROSS MULTIPLY
10(R^2-900)=1440R
10R^2-1440R-9000=0
10(R^2-144R-900)=0
10(R-150)(R+6)=0
5-150=0
R=150 ANSWER FOR THE SPEED OF THE AIRPLANE.
PROOF
10=720/(150-30)+720/(150+30)
10=720/180+720/120
10=4+6
10=10

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