Question 1171013
rate * time = distance.


with the wind, the rate is additive.
let p equal the rate of the plane and w equal the rate of the wind.
the combined rate is (p + w).


against the wind, the rate is subtractive.
let p equal the rate of the plane and w equal the rate of the wind.
the combined rate is (p - w).


with the wind, the plane traveled 2835. miles in 4.5 hours.
the formula for that is:
(p + w) * 4.5 = 2835.


against the wind, the place traveled 2475 miles in the same amount of time.
the formula for that is:
(p - w) * 4.5 = 2475.


you have two equations that need to be solved simultaneously.
they are:
(p + w) * 4.5 = 2835.
(p - w) * 4.5 = 2475.


simplify these equations to get:
4.5 * p + 4.5 * w = 2835.
4.5 * p - 4.5 * w = 2475


add these two equations together to get:|
9 * p = 5310
solve for p to get:
p = 5310 / 9 = 590
that's the speed of the plane.


go back to the two equations that need to be solved simultaneously and replace p with 590 to get:
(p + w) * 4.5 = 2835 becomes (590 + w) * 4.5 = 2835
(p - w) * 4.5 = 2475 becomes (590 - w) * 4.5 = 2475


simplify to get:
4.5 * 590 + 4.5 * w = 2835
4.5 * 590 - 4.5 * w = 2475.


in the first of these equations, simplify and solve for w to get:
w = (2835 - 2655) / 4.5 = 40


in the second of these equations, simplify and solve for w to get:
w = (2475 - 2655) / -4.5 = 40


looks like the speed of the wind is 40 miles per hour and the speed of the plane is 590 miles per hour.


replace p and w with those values in the original equations to get:


(p + w) * 4.5 = 2835 becomes (590 + 40) * 4.5 = 2835 which becomes 630 * 4.5 = 2835 which becomes 2835 = 2835 which is true.


(p - w) * 4.5 = 2475 becomes (590 - 40) * 4.5 = 2475 which becomes 550 * 4.5 = 2475 which becomes 2475 = 2475 which is true.


your solution is that the speed of the wind is 40 miles per hour.
this solution has been confirmed to be good.