13.137. Three machines from different systems perform a certain counting task. If the entire task is assigned to only the second or the first machine, then the second machine alone will take 2 minutes longer to complete the entire task than the first machine. The third machine can complete the entire task in a time twice as long as the first machine. Since the parts of the task are similar, the entire task can be divided among the three machines. Then, working together and finishing the task simultaneously, they will complete it in 2 minutes and 40 seconds. How long will each machine take to complete this task individually?
Solution.

Let the first machine complete the work in $x$ min, the second in $y$ min, and the third in $z$ min. According to the conditions, $\left\{\begin{array}{l}y=x+2, \\ z=2 x, \\ \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{3}{8},\end{array}\right.$ from which $x=6$ min, $y=8$ min, $z=12$ min.

Answer: in 6, 8, and 12 min.