Inlet pipe A can fill a water storage sump in $6\text{ hours}$, while inlet pipe B can fill it in $12\text{ hours}$. If both pipes are opened simultaneously into an empty sump, the time required to completely fill the sump is ________ $\text{hours}$ (round off to two decimal places).
Answer Key:
4.00
Step-by-Step Solution & Explanation
Combined filling rate of both pipes:
$\text{Rate} = \frac{1}{T_A} + \frac{1}{T_B} = \frac{1}{6} + \frac{1}{12} = \frac{2 + 1}{12} = \frac{3}{12} = \frac{1}{4}\text{ per hour}$
Total time to fill:
$T = 4.00\text{ hours}$