<PRE><B>Question 1137928</B>
r * t = d
r = rate
t = time
d = distance


plane flies at 175 mph.


distance = 1000 miles.


plane flies with the wind in one direction and against the wind in the other direction.


it takes t hours with the wind and t + 1 hour against the wind.


w = the speed of the wind.


with the wind, the formula becomes (175 + w) * t = 1000


against the wind, the formula becomes (175 - w) * (t + 1) = 1000


since they&#39;re both equal to 1000, you get:


(175 + w) * t = (175 - w) * (t + 1)


simplify each side of this equation t0 get:


175 * t + w * t = 175 * t + 175 - w * t - w


subtract 175 * t from both sides of the equation to get:


w * t = 175 - w * t - w


add w * t to both sides of the equation to get:


2 * w * t = 175 - w


add w to both sides of the equation to get:


2 * w * t + w = 175


factor out the w to get:


w * (2t + 1) = 175


solve for w to get:


w = 175 / (2t + 1)


simplify the first equation of (175 + w) * t = 1000 to get:


175 * t + w * t = 1000


replace w with 175 / (2t + 1) to get:


175 * t + 175 / (2t + 1) * t = 1000


multiply both sides of this equation by (2t + 1) to get:


175 * t * (2t + 1) + 175 * t = 1000 * (2t + 1)


simplify further to get:


350 * t^2 + 175 * t + 175 * t = 2000 * t + 1000


combine like terms to get:


350 * t^2 + 350 * t = 2000 * t + 1000


subtract 2000 * t and subtract 1000 from both sides of the equation to get:


350 * t^2 - 1650 * t - 1000 = 0


factor this quadratic equation to get:


t = 5.257705786321 or t = -0.54342007203528


t can&#39;t be negative, so t = 5.257705786321


replace t in the first equation with 5.257705786321 to get:


(175 + w) * t = 1000 becomes (175 + w) * 5.257705786321 = 1000


simplify this equation to get 920.098512606 + 5.257705786321 * w = 1000


solve for w to get:


w = (1000 - 920.098512606) / 5.257705786321 = 15.197025212


you have:


t = 5.257705786321
w = 15.197025212


(175 + w) * t = 1000 becomes (175 + 15.197025212) * 5.257705786321 = 1000 which becomes 1000 = 1000 which is true.


(175 - w) * (t + 1) = 1000 becomes (175 - 15.197025212) * (5.257705786321 + 1) = 1000 which becomes 1000 = 1000 which is true.


solution is confirmed to be good.


your solution is that the velocity of the wind is 15.197025212 miles per hour in the original direction of the trip.












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