Answer
The average velocity of the plane is $\text{725 }{\text{km}}/{\text{h}}\;$ and the average velocity of the wind is $\text{75 }{\text{km}}/{\text{h}}\;$.
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 $2$ hours to travel $1600\text{ km}$ in the direction of wind and it takes $3$ hours to travel $1950\text{ km}$ against the direction of wind.
The equations from the table give:
$\begin{align}
& 2\left( x+y \right)=1600 \\
& x+y=800
\end{align}$ …… (1)
And
$\begin{align}
& 3\left( x-y \right)=1960 \\
& x-y=650
\end{align}$ …… (2)
Add equation (1) and equation (2).
$\begin{align}
& \underline{\begin{align}
& x+y=800 \\
& x-y=650
\end{align}} \\
& 2x\text{ }=1450 \\
& \text{ }x\text{ }=725 \\
\end{align}$
Substitute $ x=725$ in equation (1).
$\begin{align}
& x+y=800 \\
& 725+y=800 \\
& y=800-725 \\
& y=75
\end{align}$
Therefore, the average velocity of the plane is $\text{725 }{\text{km}}/{\text{h}}\;$ and the average velocity of the wind is $\text{75 }{\text{km}}/{\text{h}}\;$.
