An artificial lake with a volume of $9900 \mathrm{~m}^{3}$ can be filled with water through two pipes. If the first pipe is open for 10 hours and the second for 14 hours, the lake fills up; it also fills up if the first pipe is open for 18 hours and the second for 12 hours. How long do both pipes need to be open equally to fill the lake?
To find the sought time, we do not need the specific amount of water. We denote this amount by $m$, then

$$
10 x+14 y=m
$$

$$
18 x+12 y=m
$$

$$
(x+y)=m
$$

Dividing (1) by (2), (2) by (3), and adding the resulting equations:

$$
\begin{gathered}
11 x+11 y=\frac{m}{2}+\frac{m}{3}=\frac{5 m}{6} \\
(x+y)=\frac{5 m}{66}
\end{gathered}
$$

Substituting (4) into (3):

$$
\frac{5 m t}{66}=m
$$

and thus

$$
t=\frac{66}{5}=13 \text{ hours } 12 \text{ minutes. }
$$

(Frigyes Riesz, fógymn. VIII. o.t., Györ.)

The problem was also solved by: Béla Bálint, Jenő Fekete, Mór Feuer, Antal Freund, Bernát Friedmann, Gyula Friedman, Emil Geist, Zsigmond Goldstein, Béla Grünhut, Ervin Hofbauer, Tivadar Hönigsfeld, Nándor Kántor, Béla Kiss, Mór Klein, Ödön Kornis, Béla Schneider, Károly Szabó, Aladár Tauszig.