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 ->  Polynomials-and-rational-expressions -> 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


   

Question 90884: 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?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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?
--------------
Let the speed of the plane in calm air be "p".
---------------------
Against the wind DATA:
distance = 720 mi ; rate = p-30 ; time = d/r = 720/(p-30)
---------------
With the wind DATA;
distance = 720 mi ; rate = p+30 ; time = d/r = 720/(p+30)
------------------
EQUATION:
time + 1ime = 10 hrs.
720/(p-30) + 720/(p+30) = 10
72/(P-30) + 72/(p+30) = 1
Multiply thru by P^2-900 to get:
72(p+30) + 72(p-30) = p^2-900
144p= p^2-900
p^2-144p-900 = 0
(p+6)(p-150)=0
p = 150 mph (speed of the plane in still air)
===============
Cheers,
Stan H.