#### Answer

The time needed for both pipes together is $6\frac{2}{3}$ hours.

#### Work Step by Step

Let $x$ hours be the time needed for both pipes to fill the tank together and $C$ be the total capacity of the tank
Since the first inlet pipe can fill the tank in 12 hours, the capacity amount that it can fill in 1 hour is $\frac{1}{12}C$
For the second pipe, it can fill the tank in 15 hours, so the capacity amount that it can fill in 1 hour is $\frac{1}{15}C$
Now, if both pipes are used to fill the tank together, the equation will be
$(\frac{1}{12}C$ + $\frac{1}{15}C) \cdot x = C$
$(\frac{1}{12}$ + $\frac{1}{15}) \cdot x = 1$
$(\frac{15 + 12}{180}) x = 1$
$x = \frac{180}{27}$
$x = \frac{20}{3}$
$x = 6\frac{2}{3}$
The time needed for both pipes together is $6\frac{2}{3}$ hours.