SOLUTION: please help me love this question A plane flies 490 miles with the wind and 310 miles against the wind in the same length of time. If the average velocity of the wind is 27 mph, wh

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Question 1006534: please help me love this question A plane flies 490 miles with the wind and 310 miles against the wind in the same length of time. If the average velocity of the wind is 27 mph, what is the average velocity of the plane in still air?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = the average speed of the
plane in still air
+p+%2B+27+ = the average speed of the
plane flying with the wind
+p+-+27+ = the average speed of the
plane flying against the wind
Let +t+ = time in hrs
--------------------------------
Equation for flying with the wind:
(1) +490+=+%28+p+%2B+27+%29%2At+
Equation for flying against the wind:
(2) +310+=+%28+p+-+27+%29%2At+
--------------------------------
(1) +t+=+490+%2F+%28+p+%2B+27+%29+
Substitute this result into (2)
(2) +310+=+%28+p+-+27+%29%2A%28+490+%2F+%28+p+%2B+27+%29+%29+
Multiply both sides by +p+%2B+27+
(2) +310%2A%28+p+%2B+27+%29+=+490%2A%28+p+-+27+%29+
(2) +310p+%2B+8370+=+490p+-+13230+
(2) +180p+=+21600+
(2) +p+=+120+
-----------------
The plane's speed in still air is 120 mi/hr
------------------
check:
(1) +490+=+%28+p+%2B+27+%29%2At+
(1) +490+=+%28+120+%2B+27+%29%2At+
(1) +490+=+147t+
(1) +t+=+3.333+ hrs ( 1 hr 20 min )
and
(2) +310+=+%28+p+-+27+%29%2At+
(2) +310+=+%28+120+-+27+%29%2At+
(2) +310+=+93t+
(2) +t+=+3.333+ hrs
OK