.Explanation
Let the speed of the still wind be V
let the speed of the wind be W
From the first statement
[tex]\begin{gathered} v+w=\frac{1342}{5.5} \\ \end{gathered}[/tex]From the second statement
[tex]v-w=\frac{1078}{5.5}[/tex]The value of v and w will be obtained by solving using the elimination method
[tex]\begin{gathered} \text{Adding both equations} \\ v+v+w-w=\frac{1342}{5.5}+\frac{1078}{5.5} \end{gathered}[/tex]Thus
[tex]\begin{gathered} 2v=\frac{1342+1078}{5.5} \\ \\ 2v=\frac{2420}{5.5} \\ \\ v=\frac{2420}{11} \\ \\ v=220 \end{gathered}[/tex]Then to get W
[tex]\begin{gathered} v+w=\frac{1342}{5.5} \\ \\ w=\frac{1342}{5.5}-v \\ \\ w=\frac{1342}{5.5}-220 \\ \\ w=24 \end{gathered}[/tex]Therefore, the speed of the jet in the still air is 220 miles per hour
The speed of the wind is 24 miles per hour
