2. Five people are performing a certain task. The first, second, and third, working together, complete the work in the same time as the second, fourth, and fifth. The first, working with the fifth, completes the work in the same time as the third, working with the fourth, which is 2 hours. How long will it take for all five people to complete the work together? (15 points)
Solution:

Let V be the volume of work, $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ be the speed of completing the work respectively.

$$
\left\{\begin{array} { c } 
{ ( x _ { 1 } + x _ { 2 } + x _ { 3 } ) * 1 = V } \\
{ ( x _ { 2 } + x _ { 4 } + x _ { 5 } ) * 1 = V } \\
{ ( x _ { 1 } + x _ { 5 } ) * 2 = V } \\
{ ( x _ { 3 } + x _ { 4 } ) * 2 = V }
\end{array} \quad \left\{\begin{array}{c}
x_{1}+x_{2}+x_{3}=V \\
x_{2}+x_{4}+x_{5}=V \\
x_{1}+x_{5}=\frac{V}{2} \\
x_{3}+x_{4}=\frac{V}{2}
\end{array}\right.\right.
$$

Add all the equations. We get:

$$
\begin{aligned}
& 2 x_{1}+2 x_{2}+2 x_{3}+2 x_{4}+2 x_{5}=3 V \\
& 2\left(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}\right)=3 V
\end{aligned}
$$

The required time $t=\frac{V}{\left(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}\right)}$, then $\frac{V}{\left(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}\right)}=\frac{2}{3}$.
$t=\frac{2}{3}$ hours $=40$ minutes.

Answer: $\frac{2}{3}$ hours (40 minutes)