SOLUTION: An airplane flies 1000 miles in two hours. The return flight against the wind took 2.5 hours. Find the airplane's speed in still air and the speed of the wind.

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Question 953679: An airplane flies 1000 miles in two hours. The return flight against the wind took 2.5 hours. Find the airplane's speed in still air and the speed of the wind.
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Since it takes 2 hours to cover 1000 miles, that is 1000/2 = 500 mile per hour. And coming back against the same wind, the speed is 1000/2.5 = 400 miles per hour.
Let a be the air speed and w the wind speed:
a + w = 500
a – w = 400 Let’s add the two equations:
a + w + a – w = 500 + 400 Complete the additions on both sides:
2a = 900
a = 900/2
a = 450 is the plane’s speed in still air. Now substitute in the first equation:
450 + w = 500 Subtract 450 on both sides
w = 50 is the wind speed