SOLUTION: Need your help again. Question: A plane flies a distance of 2900 miles. With the tailwind, it averaged 600 mph. When the wind changed from a tailwind to a headwind, the speed dr

Question 258129: Need your help again. Question: A plane flies a distance of 2900 miles. With the tailwind, it averaged 600 mph. When the wind changed from a tailwind to a headwind, the speed dropped to 550 mph. Total trip time is 5 hours. Determine the length of time it flew at each speed.
My solution was: x/600 + 2900 - x/550 = 5, which didn't work. Thanks!!
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
This is an RTD problem. Here is a table based on the given information:
PLANE . . . . .rate . . . . . . . . time . . . . . . . . . distance
with . . . . . r+c = 600 . . . . . . Tw . . . . . . . . . . 600Tw
against . . . . r-c = 550 . . . . . . Ta . . . . . . . . . . 550Ta
total . . . . . . . . . . . . . . . . .5 . . . . . . . . . . 2900
we have two equations:
(i)
(ii)
we simplify (ii) to be
(iii)
multiply (i) by -11 to get
(iv)
adding (iii) and (iv) we get

or 3 hours flying with the wind.
This means that

or 2 hours flying against the wind.
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