SOLUTION: An airplane flies between Boston and Cleveland. During a round-trip flight, the plane flew a distance of 630 mi each way. The trip with a tailwind took 3 hours. The return trip aga

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Question 988491: An airplane flies between Boston and Cleveland. During a round-trip flight, the plane flew a distance of 630 mi each way. The trip with a tailwind took 3 hours. The return trip agains the wind took 3.5 hours. Find the speed of the wind. Find the speed of the plane in still air
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = windspeed in mi/hr
Let +s+ = the speed of the plane in still air
+s+%2B+w+ = plane's speed going with the wind
+s+-+w+ = plane's speed going against the wind
---------------------------------------------
(1) +630+=+%28+s+%2B+w+%29%2A3+
(2) +630+=+%28+s+-+w+%29%2A3.5+
----------------------------
(1) +s+%2B+w+=+210+
(2) +s+-+w+=+180+ ( now add equations )
--------------------
+2s+=+390+
+s+=+195+
and
(1) +s+%2B+w+=+210+
(1) +195+%2B+w+=+210+
(1) +w+=+15+
-----------------
The windspeed is 15 mi/hr
The speed of th plane in still air is 195 mi/hr
------------------
check:
(1) +630+=+%28+s+%2B+w+%29%2A3+
(1) +630+=+%28+195+%2B+15+%29%2A3+
(1) +630+=+210%2A3+
(1) +630+=+630+
and
(2) +630+=+%28+s+-+w+%29%2A3.5+
(2) +630+=+%28+195+-+15+%29%2A3.5+
(2) +630+=+180%2A3.5+
(2) +630+=+630+
OK