3.55 During the unloading of 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?
3.55 Let's accept the entire volume of work as a unit. Let the more powerful crane need $x$ hours, the less powerful crane need $y$ hours, and the time for one more powerful and one less powerful crane working together be $-z$ hours. Then the corresponding productivities are $\frac{1}{x}, \frac{1}{y}$, and $\frac{1}{z}$. According to the conditions,

$$
\frac{8}{x}+\left(\frac{4}{x}+\frac{2}{y}\right) 3=1 ; \frac{4}{x}+\frac{2}{y}=\frac{1}{4.5} ; \frac{1}{x}+\frac{1}{y}=\frac{1}{z}
$$

Solving this system, we find $x=24, y=36, z=14.4$.

Answer: $\quad 3 \mathbf{1 4 , 4} 4$ hours.