13.140. On one of two machines, a batch of parts is processed 3 days longer than on the other. How many days would it take for each machine to process this batch of parts separately, if it is known that when working together, these machines processed a batch of parts three times larger in 20 days?
Solution.

Time $(t)$, the amount of work done per unit of time, i.e., productivity ( $W$ ), and the total volume of work ( $V$ ) are related by $V=W t$. Let $V=1$ and fill in the following table:

| Machine | Time, days | Volume of work | Productivity |
| :---: | :---: | :---: | :---: |
| First | $x$ | 1 | $\frac{1}{x}$ |
| Second | $x-3$ | 1 | $\frac{1}{x-3}$ |
| Both together | 20 | 3 | $\frac{3}{20}$ |

Since the productivity of the machines adds up when they work together, $\frac{1}{x}+\frac{1}{x-3}=\frac{3}{20}$, from which $x=15$.

Answer: 15 and 12 days.