## 123. Math Puzzle $8 / 75$

Young Pioneers are painting the $36 \mathrm{~m}$ long fence of the school grounds. They had planned a certain amount of time for this. However, since they paint $0.20 \mathrm{~m}$ more of the fence per hour than planned, they will finish two hours earlier.

How many hours do they need for the work?
The Young Pioneers need $x$ hours to paint the fence at a productivity of $y \frac{\mathrm{m} \text { fence }}{\mathrm{hour}}$. Therefore, $x \cdot y=36$.

A longer time by two hours was planned with a productivity reduced by $0.2 \frac{\mathrm{m} \text { fence }}{\text { hour }}$: $(x+2)(y-0.2)=36$

With $y=\frac{36}{x}$, this results in

$$
\begin{gathered}
36-0.2 x+\frac{2 \cdot 36}{x}-0.4=36 \quad \text { or } \\
x^{2}+2 x-360=0 \quad, \quad x=-1 \pm \sqrt{1+360}=-1 \pm 19
\end{gathered}
$$

sensible solution $x=18$. The Young Pioneers need 18 hours.