Question 719418
Let x be the speed of the wind. Then 75+x is the speed of the plane flying with the wind and 300/(75+x) is the amount of time the plane flew with the wind. Similarity 75-x is the speed of the plane flying against the wind and 300/;(75-x) is the amount of time the plane flew against the wind. As we are given that the amount of time the plane flew with and against the wind is 9 hours we have that
300/(75+x)+300/(75-x)=9
(75+x)*(75-x)*300/(75+x) + (75+x)*(75-x)*300/(75-x)=(75+x)*(75-x)*9
(75-x)*300 + (75+x)*300=(75+x)*(75-x)*9
22500-300*x + 22500+300*x=(5625-x^2)*9
45000=50625-9*x^2
9*x^2-5625=0
(3*x)^2-75^2=0
(3*x-75)*(3*x+75)=0
3*x-75=0, 3*x+75=0
x=25, x=-25
As the speed of the wind must be positive we know it is 25.