SOLUTION: An airplane travels 600 miles against the wind in 3.5 hours and makes the return trip (with the wind) in 2.5 hours. Find the rate of the wind

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Question 226232: An airplane travels 600 miles against the wind in 3.5 hours and makes the return trip (with the wind) in 2.5 hours. Find the rate of the wind
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = rate of airplane
Let w = rate of wind
s+%2B+w = rate flying with the wind
s+-+w = rate flying against the wind
given:
t+=+2.5 hrs with the wind
t+=+3.5 hrs against the wind
d+=+600 mi
---------------
I can now write equations
600+=+%28s+%2B+w%29%2A2.5
600+=+%28s+-+w%29%2A3.5
This is 2 equations and 2 unknowns, so it's solvable
2.5s+%2B+2.5w+=+600
3.5s+-+3.5w+=+600
Multiply both equations by 10
25s+%2B+25w+=+6000
35s+-+35w+=+6000
Divide both equations by 5
5s+%2B+5w+=+1200
7s+-+7w+=+1200
Multiply the 1st equation by 7 and
the 2nd equation by 5
35s+%2B+35w+=+8400
35s+-+35w+=+6000
Add the equations
70s+=+14400
s+=+205.71
and, since
5s+%2B+5w+=+1200
5%2A205.71+%2B+5w+=+1200
5w+=+1200+-+1028.57
5w+=+171.429
w+=+34.29
The wind speed is 34.29 mi/hr
check:
600+=+%28s+%2B+w%29%2A2.5
600+=+%28205.71+%2B+34.29%29%2A2.5
600+=+239.996%2A2.5
600+=+599.989 close enough
and
600+=+%28s+-+w%29%2A3.5
600+=+%28205.71+-+34.29%29%2A3.5
600+=+171.42%2A3.5
600+=+599.97 close enough