Question 1141756
going with the wind, the equation is (r + w) * t = d
going against the wind, the equation is (r - w) * t = d


r is the rate of the plane.
w is the rate of the wind.
t is the time.
d is the distance.


d is equal to 1980.
going with the wind, t = 4.5 hours.
going against the wind, t = 5.5 hours.


the equations become:


(r + w) * 4.5 = 1980
(r - w) * 5.5 = 1980


simplify to get:


4.5 * r + 4.5 * w = 1980
5.5 * r - 5.5 * w = 1980


multiply both sides of the first equation by (5.5 / 4.5) and leave the second equation as is to get:


5.5 * r + 5.5 * w = 2420
5.5 * r - 5.5 * w = 1980


subtract the second equation from the first to get:


11 * w = 440


solve for w to get w = 40.


replace w with 40 in the first original equation to get:


(r + w) * 4.5 = 1980 becomes (r + 40) * 4.5 = 1980


simplify to get 4.5 * r + 180 = 1980


subtract 180 from both sides to get 4.5 * r = 1980 - 180


combine like terms to get 4.5 * r - 1800


solve for r to get r = 400.


you have the rate (speed) of the plane = 400 miles per hour and the rate (speed) of the wind = 40 miles per hour.


going with the wind, the combined rate is 440 miles per hour * 4.5 hours = 1980 miles.


going against the wind, the combined rate is 360 miles per hour * 5.5 hours = 1980.


the numbers look good.


your solution is that the speed of the plane is 400 miles per hour and the speed of the wind is 40 miles per hour (rate and speed mean the same thing in this problem).