13.312. When unloading a barge, four lifting cranes of the same power initially worked for 2 hours. Then, two additional cranes of lesser but equal power were put into operation. After this, it took another 3 hours to complete the unloading. If all these cranes had started working simultaneously, the unloading would have been completed in 4.5 hours. If one crane of greater power and one crane of lesser power worked together, how long would it take them to unload the barge?
Solution.

Let's assume the entire volume of work is 1. Let the time required for the more powerful crane to complete the work alone be $x$ days, for the less powerful crane be $y$ days, and for one more powerful and one less powerful crane working together be $-z$ days. The work efficiency is then $\frac{1}{x}, \frac{1}{y}$, and $\frac{1}{z}$, respectively. According to the problem, we have the system of equations:

$$
\left\{\begin{array}{l}
\frac{8}{x}+\left(\frac{4}{x}+\frac{2}{y}\right) \cdot 3=1 \\
\frac{4}{x}+\frac{2}{y}=\frac{1}{4.5}, \quad \\
\frac{1}{x}+\frac{1}{y}=\frac{1}{z}
\end{array} \quad \text { from which } x=24, y=36, z=14.4\right.
$$

Answer: in 14.4 hours.