#### Answer

The average velocity of the plane is $630\text{ mph}$ and the average velocity of the wind is $90\text{ mph}$.

#### Work Step by Step

Consider the average velocity of the plane to be $ x $ and the average velocity of the wind to be $ y $.
The average velocity of the plane in the direction of the wind is $ x+y $ and the average velocity against the wind is $ x-y $.
A plane takes $3$ hours to fly $2160$ miles in the direction of the wind and it takes $4$ hours to fly the same distance against the direction of the wind.
Form the equations in the table:
$\begin{align}
& 3\left( x+y \right)=2160 \\
& x+y=720
\end{align}$ …… (1)
And
$\begin{align}
& 4\left( x-y \right)=2160 \\
& x-y=540
\end{align}$ …… (2)
Add equation (1) and equation (2).
$\begin{align}
& \underline{\begin{align}
& x+y=720 \\
& x-y=540
\end{align}} \\
& 2x\text{ }=1260 \\
& \text{ }x\text{ }=630 \\
\end{align}$
Substitute $ x=630$ in equation (1).
$\begin{align}
& x+y=720 \\
& 630+y=720 \\
& y=720-630 \\
& y=90
\end{align}$
Therefore, the average velocity of the plane is $630\text{ mph}$ and the average velocity of the wind is $90\text{ mph}$.