SOLUTION: A plane traveled 2655 miles with the wind in 4.5 hours and 2115 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the win

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Question 1099330: A plane traveled 2655 miles with the wind in 4.5 hours and 2115 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the plane in still air
Let +w+ = the speed of the wind
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Flying with the wind:
(1) +2655+=+%28+s+%2B+w+%29%2A4.5+
Flying against the wind:
(2) +2115+=+%28+s+-+w+%29%2A4.5+
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Add the equations
(1) +4.5s+%2B+4.5w+=+2655+
(2) +4.5s+-+4.5w+=+2115+
--------------------------------
+9s+=+4770+
+s+=+530+
and
(1) +4.5s+%2B+4.5w+=+2655+
(1) +4.5%2A530+%2B+4.5w+=+2655+
(1) +2385+%2B+4.5w+=+2655+
(1) +4.5w+=+270+
(1) +w+=+60+
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The speed of the plane in still air is 530 mi/hr
The speed of the wind is 60 mi/hr
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check:
(1) +2655+=+%28+530+%2B+60+%29%2A4.5+
(1) +2655+=+590%2A4.5+
(1) +2655+=+2655+
You can check (2)