Answer
See the explanation
Work Step by Step
Speed of the man $x$
Speed of the wind $y$
Speed when flying in a head wind $x-y$
Speed when flying back $x+y$
-Speed flying in a head wind $\times$ time flying in a head wind $=$ distance flown in a head wind.
$(x-y)\times2=180$.
-Speed flying back $\times$ time flying back $=$ distance flown back.
$(x+y)\times\frac{6}{5}=180$.
Therefore,
$\begin{cases}
2x-2y=180\\
\frac{6}{5}x+\frac{6}{5}y=180
\end{cases}$
Multiplying the second equation by 5.
$\begin{cases}
2x-2y=180\\
6x+6y=900
\end{cases}$
Multiplying the first equation by 3 and adding it together.
$\begin{cases}
6x-6y=540\\
6x+6y=900\\
-- -- -- -\\
12x=1440
\end{cases}$
Thus, $x=120$. Substituting back in $\frac{240-180}{2}=y, y=30$
