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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A plane flies 720 miles against a steady 30 mi/hr headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the plane’s speed in still a      Log On


   

Question 65329: A plane flies 720 miles against a steady 30 mi/hr headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the plane’s speed in still air?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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A plane flies 720 miles against a steady 30 mi/hr headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the plane’s speed in still air?
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Let p be plane speed
Against the wind DATA:
distance= 720 miles ; Rate= p-30 mph ; time = d/r= 720/(p-30) hrs.
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With the wind DATA:
distance =720 miles ; rate = p+30 mph ; time = d/r = 720/(p+30) hrs.
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EQUATION:
time with + time against = 10 hrs
720/(p+30) + 720/(p-30)= 10
Divide thru by 720 to get:
1/(p+30) + 1/(p-30)= 1/72
Multiply thru by (p+30)(p-30) to get:
p-30+p+30=(1/72)(p^2-900)
Simplify the left side to get:
2p=(1/72)(p^2-900)
Multiply both sides by 72 to get:
144p=p^2-900
Rearrange:
p^2-144p-900=0
Use the quadratic formula to get:
p=[144+-sqrt(144^2-4*-900)]/2
p=[144+-156]/2
Select the positive solution to get:
p=[144+156]/2=300/2=150 mph
Cheers,
Stan H.