SOLUTION: Flying against the wind, it took a pilot 1/2 hour longer to travel 500 miles than it took flying with the wind. The rate of the plane in calm air is 225 mph. Find the rate of the

Question 769537: Flying against the wind, it took a pilot 1/2 hour longer to travel 500 miles than it took flying with the wind. The rate of the plane in calm air is 225 mph. Find the rate of the wind.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the rate of the wind
Flying with the wind, the plane's rate is:

Flying against the wind, the plane's rate is:

---------------
Equation flying with the wind:
(1)
Flying against the wind:
(2)
------------------------------
(2)
(2)
(2)
-------------------------------
(1)
(1)
(1)
----------------------
Substitute (1) into (2)
(2)
(2)
(2)
(2)
(2)
(2)
Use quadratic formula

( can't use the negative root )

and, since
(1)
(1)
(1)
(1)
(1)
The rate of the wind is 25 mi/hr
check:
(2)
(2)
(2)
(2)
OK

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