recall your d = rt, distance = rate * time.
w = rate of the wind
225 = rate of the plane
so the plane flies 260 miles in say "t" hours, with the wind, now, the plane is not really going 225 mph fast, is really going "225 + w" fast because the wind is adding speed to it, likewise, when going against the wind, is not going 225 mph fast is going "225 - w" because the wind is eroding speed from it, and that was also covered in "t" hours
[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \stackrel{downwind}{\textit{with the wind}}&260&225+w&t\\ \stackrel{\textit{upwind}}{\textit{against the wind}}&190&225-w&t \end{array}~\hfill \begin{cases} 260=(225+w)t\\\\ \cfrac{260}{225+w}=\boxed{t}\\\\ \cline{1-1}\\ 190=(225-w)t \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{substituting \underline{t} in the 2nd equation}}{190=(225-w)\left( \boxed{\cfrac{260}{225+w}} \right)}\implies \cfrac{190}{225-w}=\cfrac{260}{225+w} \\\\\\ 42750+190w=58500-260w\implies 190w=15750-260w \\\\\\ 450w=15750\implies w=\cfrac{15750}{450}\implies \blacktriangleright w=35 \blacktriangleleft[/tex]
