Final answer:
It will take 8 hours to fill the pool with a leak, considering the fill rate is 1 pool/6 hours and the leak rate is 1 pool/24 hours. The net rate of filling is calculated by subtracting the leak rate from the fill rate, resulting in a net fill time of 8 hours.
Step-by-step explanation:
The student's question is about determining how long it will take to fill a swimming pool with a leak if it normally takes 6 hours to fill it and 24 hours for it to empty due to the leak. To find the answer, we use the concept of rates. The filling rate is one pool per 6 hours (1/6 pool/hour), and the leaking rate is one pool per 24 hours (1/24 pool/hour).
To find the combined rate when the pool is being filled while leaking, we subtract the leak rate from the fill rate:
Net rate = Fill rate - Leak rate
Net rate = (1/6 - 1/24) pools/hour
Net rate = (4/24 - 1/24) pools/hour
Net rate = (3/24) pools/hour
Net rate = (1/8) pools/hour
Next, we find out how long it takes to fill the pool at this net rate:
Time to fill = 1 / Net rate
Time to fill = 1 / (1/8) hours
Time to fill = 8 hours
Therefore, the correct answer is B) It will take 8 hours to fill the empty pool.