Question 630014
Lets pretend that the speed of the wind is x. So the speed of the plane that is going 400 mph is 400+x. And the speed of the plane going 450 mph is 450-x. The formula for travel and distance problems is distance= speed*time, which is the same thing as time= distance/speed. So the time the plane with the wind took was {{{1250/(400+x)}}} and the time that the plane against the wind took was {{{1000/(450-x)}}} and since they are the same, we should set them equal to form an equation. 
{{{1250/(400+x)=1000/(450-x)}}}
So if we multiply both sides by the LCD(least common denominator),{{{x^2+50x+180000}}}, we get 
{{{-1250x+562500=1000x+400000}}}
So if we subtract 400000 and add 1250x to each side, we get
{{{162500=2250x}}}
Now if we divide by 2250, we get
{{{72.22222= x}}}
So the speed of the wind is 72.22 mph.