SOLUTION: Assume that a plane is flying at a constant speed under unvarying wind conditions. Traveling against a head wind, it takes the plane 4 hours to travel 1540 miles. Traveling with

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Question 545202: Assume that a plane is flying at a constant speed under
unvarying wind conditions. Traveling against a head
wind, it takes the plane 4 hours to travel 1540 miles.
Traveling with a tail wind, the plane flies 1365 miles in 3
hours. Find the speed of the plane and the speed of the
wind.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = wind speed
Let s = speed of plane with no wind
+s+-+w+ = plane's speed against wind
+s+%2B+w+ = plane's speed with the wind
----------
given:
(1) +1540+=+%28+s+-+w+%29%2A4+
(2) +1365+=+%28+s+%2B+w+%29%2A3+
-------------------
(1) +1540+=++4s+-+4w++
(2) +1365+=++3s+%2B+3w+
Divide both sides of (1) by 4 and
divide both sides of (2) by 3
Then add the equations
(1) +385+=+s+-+w+
(2) +455+=+s+%2B+w+
+2s+=+840+
+s+=+420+
and
(1) +385+=+s+-+w+
(1) +385+=+420+-+w+
(1) +w+=+420+-+385+
(1) +w+=+35+
the plane's speed in still air is 420 mi/hr
The wind's speed is 35 mi/hr
check:
(1) +1540+=+%28+s+-+w+%29%2A4+
(1) +1540+=+%28+420+-+35+%29%2A4+
(1) +1540+=+385%2A4+
(1) +1540+=+1540+
OK