Answer
The average velocity of the plane in still air is $650$ mph and that of the wind is $50$ 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 is $y$ mph.
Step 2. When flying with the wind, the total average velocity is $x+y$; thus $6(x+y)=4200$ or $x+y=700$
Step 3. When flying against the wind, the resulting average velocity is $x-y$; thus $7(x-y)=4200$ or $x-y=600$
Step 4. Add the two equations; we get $2x=1300$. Thus $x=650$ mph and $y=50$ mph.
