Question 597328: An airplane traveling with the wind flies 450 miles in 2 hours. On the return trip, the plane takes 3 hours to travel the same distance. Find the speed of the airplane if the wind is still.
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Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! An airplane traveling with the wind flies 450 miles in 2 hours.
On the return trip, the plane takes 3 hours to travel the same distance.
Find the speed of the airplane if the wind is still.
:
Let s = effective speed of the airplane in still air
Let w = speed of the wind
:
Write a distance equation for each way:
2(s+c) = 450
3(s-c) = 450
:
We can simplify both equations, divide the 1st eq by 2, divide the 2nd by 3, results:
s + c = 225
s - c = 150
----------- adding eliminates c, find s
2s = 375
s = 375/2
s = 187.5 mph in still air
:
:
To check this out, find the speed of the wind
187.5 + c = 225
c = 225 - 187
c = 37.5 mph is the speed of the wind
:
Check the distance using these value for s and c
2(187.5+37.5) =
2(225) = 450 mi
and
3(187.5-37.5) =
3(150) = 450
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