2. A tank is filled by 2 pipes. Together, the two pipes fill the tank in 12 hours. If the first pipe fills the tank by itself to half, and then the second pipe continues to fill the tank by itself, the entire tank will be filled in 25 hours. How long does it take for each pipe to fill the tank by itself?
Solution. Let $x$ be the number of hours it takes for the first pipe to fill the tank on its own, and $y$ be the number of hours it takes for the second pipe to fill the tank on its own. From the conditions of the problem, we get the following system of equations

$$
\left\{\begin{array}{l}
\frac{12}{x}+\frac{12}{y}=1 \\
\frac{x}{2}+\frac{y}{2}=25
\end{array}\right.
$$

From the second equation, we get $y=50-x$, and if we substitute this into the first equation, we obtain the quadratic equation

$$
x^{2}-50 x+600=0
$$

The solutions to this equation are $x_{1}=20, x_{2}=30$. Therefore, the first pipe fills the tank in 20 (30) hours, and the second pipe in 30 (20) hours.