SOLUTION: A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, t

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Question 1050351: A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing?
Found 2 solutions by advanced_Learner, Alan3354:
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
solve
90=u-v
150=u+v

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cu+%2B+-1%5Cv+=+90%2C%0D%0A++++1%5Cu+%2B+1%5Cv+=+150+%29%0D%0A++We'll use substitution. After moving -1*v to the right, we get:
1%2Au+=+90+-+-1%2Av, or u+=+90%2F1+-+-1%2Av%2F1. Substitute that
into another equation:
1%2A%2890%2F1+-+-1%2Av%2F1%29+%2B+1%5Cv+=+150 and simplify: So, we know that v=30. Since u+=+90%2F1+-+-1%2Av%2F1, u=120.

Answer: system%28+u=120%2C+v=30+%29.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing?
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Find the 2 groundspeeds upwind and downwind using d = r*t
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The plane's airspeed is the average of the 2.
Windspeed = difference between airspeed and groundspeed.