Answer
Plane: 120 mi/h
Wind: 30 mi/h
Work Step by Step
Speed is the ratio of distance and the time ,$v=\displaystyle \frac{d}{t}$.
From $v=\displaystyle \frac{d}{t}$it follows that $d=vt\qquad (*)$
Let $v$ be the speed of the plane in still air.
Let $w $ be the speed of the wind.
When flying into the headwind, the speed is $ v-w$
and time spent is $t=2$ hours
So, we have by (*)
$180=2(v-w)$
When the plane flies in the same direction as the wind, the speed is $v+w$
The time is $t=1$h 12min=($1+\displaystyle \frac{12}{60}$) h $=1.2$ h
So, we have by (*)
$180=1.2(v+w)$
$\left\{\begin{array}{ll}
180=2v-2w & /\times 1.2\\
180=1.2v+1.2w & /\times 2
\end{array}\right.$
(we are solving by elimination, eliminating w)
$\left\{\begin{array}{ll}
216=2.4v-2.4w & \\
360=2.4v+2.4w & /add
\end{array}\right.$
$576=4.8v\qquad/\div 4.8$
$\displaystyle \frac{576}{4.8}=v$
$v=$120 mi/h
Back-substitute:
$180=2v-2w$
$180=2(120)-2w$
$180=240-2w\quad/-240$
$-60=-2w\quad/\div(-2)$
$30=w$
w= 30 mi/h
