Question 415704
rate * time = distance


w = speed of the wind
r = speed of the airplane
r+w = speed of the airplane with the wind
r-w = speed of the airplane against the wind.


with the wind, the equation becomes:


6*(r+w) = 4500


against the wind, the equation becomes:


10*(r-w) = 4500


since they both equal to 4500, then they both equal to each other, so we get:


6*(r+w) = 10*(r-w)


simplify to get:


6r + 6w = 10r - 10w


subtract 6r from both sides of this equation and add 10w to both sides of this equation to get:


4r = 16w


divide both sides of this equation by 4 to get:


r = 4w


substitute 4w for r in either equation to solve for w.


first equation is:


6*(r+w) = 4500


substitute to get:


6 * (4w + w) = 4500


combine like terms to get:


6 * 5w = 4500


solve to get:


w = 4500 / 30 = 150


since r = 4w, then r must be equal to 600


you have r = 600 and w = 150


substitute in the second equation to see if that equation is true.


10*(600-150) = 4500


combine like terms to get 10*(450) = 4500 which is true.


the values of r and w are good.


the plane travels at 600 miles per hour and the wind travels at 150 miles per hour.


the answer to the question is that the wind speed is 150 miles per hour.