2. Three 3D printers print a given model that can be assembled from multiple parts. If the first and second printers were to print simultaneously, it would take them a total of 30 minutes to print the entire model. If the first and third printers were to print simultaneously, it would take them 40 minutes to print the entire model. The second and third printers would take 24 minutes to print the entire model simultaneously. How long would it take each printer to print the entire given model on its own?
2. The first printer needs $p$ minutes to print an entire model, the second printer needs $d$ minutes, and the third printer needs $t$ minutes.

Then, in one minute:

- the first and second printers would print: $\frac{1}{p}+\frac{1}{d}=\frac{1}{30}$ of a model;
- the first and third printers would print: $\frac{1}{p}+\frac{1}{t}=\frac{1}{40}$ of a model;
- the second and third printers would print: $\frac{1}{d}+\frac{1}{t}=\frac{1}{24}$ of a model.

If we sum all three equations, we get:

$\frac{1}{p}+\frac{1}{d}+\frac{1}{p}+\frac{1}{t}+\frac{1}{d}+\frac{1}{t}=\frac{1}{30}+\frac{1}{40}+\frac{1}{24}=\frac{4+3+5}{120}=\frac{12}{120}=\frac{1}{10} \Rightarrow \frac{1}{p}+\frac{1}{d}+\frac{1}{t}=\frac{1}{20}$

If we subtract each of the initial equations from the obtained sum, we get:

$\frac{1}{p}+\frac{1}{d}+\frac{1}{t}-\frac{1}{p}-\frac{1}{d}=\frac{1}{20}-\frac{1}{30} \Rightarrow \frac{1}{t}=\frac{1}{60} \Rightarrow t=60$ minutes

$\frac{1}{p}+\frac{1}{d}+\frac{1}{t}-\frac{1}{p}-\frac{1}{t}=\frac{1}{20}-\frac{1}{40} \Rightarrow \frac{1}{d}=\frac{1}{40} \Rightarrow d=40$ minutes;

$\frac{1}{p}+\frac{1}{d}+\frac{1}{t}-\frac{1}{d}-\frac{1}{t}=\frac{1}{20}-\frac{1}{24} \Rightarrow \frac{1}{p}=\frac{1}{120} \Rightarrow p=120$ minutes.

To print the entire specified model individually, the first printer needs 120 minutes, the second printer needs 40 minutes, and the third printer needs 60 minutes.