## Algebra: A Combined Approach (4th Edition)

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