SOLUTION: A plane flies 900km with a tail wind in 3 hours. The same plane takes 4 hours to make the return trip against the wind. What is the speed of the plane in still air?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A plane flies 900km with a tail wind in 3 hours. The same plane takes 4 hours to make the return trip against the wind. What is the speed of the plane in still air?      Log On


   

Question 184163: A plane flies 900km with a tail wind in 3 hours. The same plane takes 4 hours to make the return trip against the wind. What is the speed of the plane in still air?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=speed of the plane in still air
Let s=speed of the wind
If the plane is flying with the wind, we add the wind speed;
Against the wind, we subtract. So:
r+s=900/3=300------------------------------eq1
r-s=900/4=225------------------------------eq2
add eq1 and eq2:
2r=525
r=262.5 mph---------------------speed of plane in still air
substitute r=262.5 mph into eq1:
262.5+s=300
s=300-262.5=37.5 mph-------------speed of the wind
Hope this helps---ptaylor