SOLUTION: Any assistance with this word problem would be greatly appreciated. An airplane can fly with the wind a distance of 900 miles in 3 hours. However, the return trip against the wi

Question 818370: Any assistance with this word problem would be greatly appreciated.
An airplane can fly with the wind a distance of 900 miles in 3 hours. However, the return trip against the wind takes 5 hours. Find the speed of the plane in still air and the speed of the wind.

speed of the plane in still air _____________ mph
speed of the wind ___________________ mph
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
An airplane can fly with the wind a distance of 900 miles in 3 hours. However, the return trip against the wind takes 5 hours. Find the speed of the plane in still air and the speed of the wind.

speed of the plane in still air _____________ mph
speed of the wind ___________________ mph
Using distance = rate x time
Set x = speed of plane with no wind
w = wind speed
We can say
(x+w)*3 = 900
and
(x-w)*5 = 900
Rewriting the equations we have
3(x+w) = 900
5(x-w) = 900
Distribute the left had sides
3x + 3w = 900
5x - 5w = 900
Multiply the top equation by 5
Multiply the bottom equation by 3
15x + 15w = 4500
15x - 15w = 2700
Add the two equations together
30x = 7200
Divide each side by 30
x = 250
Substitute 250 into 3x + 3w = 900
3(250) + 3w = 900
750 + 3w = 900
Subtract 750 from each side.
3w = 150
w = 50
So the airplane will travel at 250 mph with no wind.
The wind speed is 50 mph.

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