Questions: 1. Three pipes can fill a pool in twelve hours. A drain can empty the full pool in eighteen hours. How many hours will it take to fill a quarter of the pool if the three pipes and the drain are open? A) 9 B) 15/2 C) 1/9 D) 1/6

Three pipes can fill a pool in twelve hours. A drain can empty the full pool in eighteen hours. How many hours will it take to fill a quarter of the pool if the three pipes and the drain are open?

Define the rates of filling and draining

Let's define the rates in terms of the fraction of the pool filled or emptied per hour:

• Three pipes together: \(\frac{1}{12}\) of the pool per hour
• Drain: \(\frac{1}{18}\) of the pool per hour

Calculate the net rate of filling

The net rate of filling when both the pipes and drain are operating is: \(\text{Net rate} = \frac{1}{12} - \frac{1}{18}\) \(\text{Net rate} = \frac{3}{36} - \frac{2}{36} = \frac{1}{36}\) of the pool per hour

Calculate the time to fill a quarter of the pool

To fill \(\frac{1}{4}\) of the pool at a rate of \(\frac{1}{36}\) of the pool per hour: \(\text{Time} = \frac{\text{Portion to fill}}{\text{Net rate}} = \frac{1/4}{1/36} = \frac{1}{4} \times 36 = 9\) hours

\(\boxed{\text{It will take 9 hours to fill a quarter of the pool.}}\)

\(\boxed{\text{The answer is A) 9}}\)