SOLUTION: A plane travels 1800 miles against a headwind in 4 hours. The return trip, now with a tailwind, takes an hour less. What is the rate of speed of the wind?

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Question 134045: A plane travels 1800 miles against a headwind in 4 hours. The return trip, now with a tailwind, takes an hour less. What is the rate of speed of the wind?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let the windspeed = w and airspeed be a.
We know distance = speed/time. The distance is the same going both ways
With the wind, the speed is a+w. The time is 4-1=3
Against the wind, the speed is a-w. The time is 4
Given:
1800+=+%28a-w%29%2A+4 --> 450+=+a+-w+ --> 450+%2Bw+=+a
1800+=+%28a%2Bw%29%2A+3
600+=+a+%2B+w
600+=+%28450+%2B+w%29+%2B+w+ using the value from the first equation above
150+=+2+w
+75+=+w
That makes airspeed = 525
Check your answer. Is 1800/(525-75) = 4? yes it is. check