A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same
amount of time it flew 300 miles against the wind. Find the speed of the wind.

The speed of the wind is 50 mile per hour  .In the question , it is given that the speed of the plane is [tex]=[/tex] 200 miles per hour .let the speed of the wind is = "w" So ,the speed of the plane with wind is [tex]=[/tex] 200 + wand the speed of the plane against  wind is [tex]=[/tex] 200 - w we know that , distance [tex]=[/tex] speed × time the plane flew "500 miles" with wind , which means , 500 [tex]=[/tex] (200 + w) × t      .....(1) and the plane flew 300 miles against the wind , which means ,300 [tex]=[/tex] (200 - w) × t       ......(2) adding both the equations , we get 800 [tex]=[/tex] t ( 200 [tex]+[/tex] w [tex]+[/tex] 200 - w)800 = t × 400t = 2 Substituting  , t = 2 in 500 [tex]=[/tex] (200 + w) × t      we get500 = (200 + w) × 2500/2 = 200 + w250 = 200 + ww = 250 - 200w = 50 Therefore , The speed of the wind is 50 mile per hour  .Learn more about Speed here https://brainly.com/question/15073313#SPJ1