<PRE><B>Question 818370</B>
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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