SOLUTION: a plane traveled 1386 miles to singapore and back. The trip there was with the wind. It took 9 hours. The trip back was into the wind. the trip back took 11 hours. Find the spe

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Question 637048: a plane traveled 1386 miles to singapore and back. The trip there was with the wind. It took 9 hours. The trip back was into the wind. the trip back took 11 hours. 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 +w+ = the speed of the wind in mi/hr
Let +p+ = the speed of the plane in still air
+p+%2B+w+ = the plane's speed going with the wind
+p+-+w+ = the plane's speed going against the wind
----------------
Equation going with the wind:
(1) +1386+=+%28+p+%2B+w+%29%2A9+
Equation going against the wind:
(2) +1386+=+%28+p+-+w+%29%2A11+
----------------------
(1) +154+=+p+%2B+w+
(1) +p+=+154+-+w+
Substitute this result into (2)
(2) +126+=+p+-+w+
(2) +126+=+154+-+w+-+w+
(2) +126+-+154+=+-2w+
(2) +-28+=+-2w+
(2) +w+=+14+
Substitute this result into (1) or (2)
(2) +126+=+p+-+14+
(2) +p+=+126+%2B+14+
(2) +p+=+140+
The plane's speed in still air is 140 mi/hr
The speed of the wind is 14 mi/hr
check:
(1) +1386+=+%28+140+%2B+14+%29%2A9+
(1) +1386+=+154%2A9+
(1) +1386+=+1386+
OK