Due to the rainstorms, our basement filled with water. To remove the water, three pumps were set up. The first pump alone could pump out the water in 3 hours, the second in 4 hours, and the third in 6 hours. After 30 minutes of working together, the second pump broke down. The remaining water was pumped out by the first and third pumps. How long did it take in total to remove the water?
$\mathrm{Az}$

|  | 1st candle | 2nd candle | 3rd candle |
| :--- | :---: | :---: | :---: |
| alone | 3 hours | 4 hours | 6 hours |
| in 1 hour | $1 / 3$ | $1 / 4$ | $1 / 6$ |

part would be waxed separately, that is,

$$
\frac{1}{2}\left(\frac{1}{3}+\frac{1}{4}+\frac{1}{6}\right)+x\left(\frac{1}{3}+\frac{1}{6}\right)=1
$$

where $x$ represents the time the first and third machines still had to work. From the equation, $x=\frac{5}{4}$ hours, so the total working time is $\frac{1}{2}+\frac{5}{4}=1 \frac{3}{4}$ hours.

The correctness of the solution can easily be verified by substitution.