Answer :
Let the following variables represent the velocities of the plane and the wind:
[tex]\begin{gathered} \text{Velocity of the plane: }v_p \\ \text{Velocity of the wind: }v_w \end{gathered}[/tex]When the plane travels with the wind, the total velocity is the sum of both velocities. When the plane travels against the wind, the resulting velocity will be the difference of both velocities.
When the plane travels with the wind, the following condition is satisfied:
[tex]v_p+v_w=\frac{880\text{ miles}}{11\text{ hours}}[/tex]When the plane travels against the wind, the following condition is satisfied:
[tex]v_p-v_w=\frac{880\text{ miles}}{20\text{ hours}}[/tex]This is a 2x2 system of equations. To solve it by the elimination method, add both equations:
[tex](v_p+v_w)+(v_p-v_w)=\frac{880\text{ miles}}{11\text{ hours}}+\frac{880\text{ miles}}{20\text{ hours}}[/tex][tex]\begin{gathered} \Rightarrow v_p+v_w+v_p-v_w=\frac{880\text{ miles}}{\text{hour}}(\frac{1}{11}+\frac{1}{20}) \\ \Rightarrow2v_p=\frac{880\text{ miles}}{\text{ hour}}(\frac{31}{220}) \\ \Rightarrow2v_p=124\cdot\frac{\text{miles}}{\text{hour}} \\ \Rightarrow v_p=62\cdot\frac{\text{ miles}}{\text{ hour}} \end{gathered}[/tex]Solve for the velocity of the wind from the first equation:
[tex]\begin{gathered} v_w=\frac{880\text{ miles}}{11\text{ hours}}-v_p \\ =\frac{880\text{ miles}}{11\text{ hours}}-62\cdot\frac{\text{miles}}{\text{hour}} \\ =18\cdot\frac{\text{miles}}{\text{hour}} \end{gathered}[/tex]Therefore, the velocity of the plane is 62 miles per hour and the velocity of the wind is 18 miles per hour.
