SOLUTION: Science and medicine. A plane flies 720 m aginst 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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Science and medicine. A plane flies 720 m aginst 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       Log On


   

Question 29434: Science and medicine. A plane flies 720 m aginst 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 for your help.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
With the wind = x+30
Against the wind = x-30

Equation:
720%2F%28x-30%29%2B720%2F%28x%2B30%29=10
720%28%28x-30%29%2B%28x%2B30%29%29=10%28%28x-30%29%28x%2B30%29%29
720%282x%29=10%28x%5E2-900%29
1440x=10x%5E2-9000
10x%5E2-1440x-9000
x%5E2-144x-900=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=%28-%28-144%29%2B-sqrt%28%28-144%29%5E2-4%2A1%2A-900%29%29%2F%282%2A1%29
simplfy, you get two solutions:

x=-6 and x=150

Remove the negative.
Hence, the speed of the plane is 150mph.
Paul.