Answer
The average velocity of the plane in still air is $130$ mph and that of the wind is $30$ mph.
Work Step by Step
Step 1. Assume the average velocity of the plane in still air is $x$ mph and that of the wind $y$ mph.
Step 2. When flying with the wind, the total average velocity is $x+y$; thus $5(x+y)=800$ or $x+y=160$
Step 3. When flying against the wind, the resulting average velocity is $x-y$; thus $8(x-y)=800$ or $x-y=100$
Step 4. Adding the two equations, we get $2x=260$; thus $x=130$ mph and $y=30$ mph.
