Answer:
[tex]7.2\; \text{hours}[/tex].
Step-by-step explanation:
Let the volume of this cistern be [tex]1[/tex].
The first pipe fills the cistern at a rate of [tex]\displaystyle \frac{1}{12\; \text{hour}}[/tex].
In other words, each hour, the first pipe would fill [tex]\displaystyle \frac{1}{12}[/tex] of the cistern every hour.
On the other hand, the second pipe fills the cistern at a rate of [tex]\displaystyle \frac{1}{18\; \text{hour}}[/tex].
This pipe would fill [tex]\displaystyle \frac{1}{18}[/tex] of the cistern every hour.
Hence, when opened together, the two pipes would fill [tex]\displaystyle \frac{1}{12} + \frac{1}{18} = \frac{3}{36} + \frac{2}{36} = \frac{5}{36}[/tex] of this cistern every hour.
At this rate, it would take [tex]\displaystyle \frac{36}{5}\; \text{hours} = 7.2\; \text{hours}[/tex] for the two pipes to fill the entire cistern.
