3.24 One of the two machines processes a batch of parts for 3 days longer than the other. How long would the processing of this batch of parts take on each machine separately, if it is known that when working together, these machines processed a batch of parts three times larger in 20 days?
3.24 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 the equation $V=W t$. 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 productivities of the machines add up when they work together, $\frac{1}{x}+\frac{1}{x-3}=\frac{3}{20}$, from which $x=15$.

Answer: 15 and 12 days.