SOLUTION: A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 30 mph, what is the speed of the plane in still air?

Question 1025505: A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 30 mph, what is the speed of the plane in still air?
Found 2 solutions by fractalier, josmiceli:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Time is distance over rate, t = d/r. We will use r for the rate in still air.
The plane's first time is t = 500/(r+30).
The plane's second time is t = 350/(r-30).
These are equal times, so

Now solve...
500(r-30) = 350(r+30)
500r - 15000 = 350r + 10500
150r = 25500
r = 170 mph
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = speed of the plane in still air in mi/hr
= the speed of the plane going with the wind
= the speed of the wind going against the wind
Let = time in hrs for both trips
----------------------------------
Equation for going against the wind
(1)
Equation for going with the wind:
(2)
----------------------------
(1)
Substitute (1) into (2)
(2)
(2)
(2)
(2)
(2)
The speed of the plane in still air is 170 mi/hr
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK
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