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Answer :
Final answer:
By calculating the rates of the large and small hoses and solving equations based on their combined rates, we determine that the smaller hose will fill the pool on its own in 120 minutes, which corresponds to option C.
Explanation:
To find the time it takes for the smaller hose to fill the pool on its own, we can use the concept of work rates. Let's assume that the larger hose has a work rate of 1 unit of work per minute. Therefore, in 65 minutes, the larger hose will complete 65 units of work. Working together, the two hoses can complete the pool in 40 minutes, so their combined work rate is 1 pool per 40 minutes.
To find the work rate of the smaller hose, we subtract the work rate of the larger hose from the combined work rate. So, the work rate of the smaller hose is 1 pool per 40 minutes - 1 pool per 65 minutes = 1 pool per 65*40 / (40-65) minutes = 1 pool per 25 minutes. Therefore, it will take the smaller house 25 minutes to fill the pool on its own. Therefore, the correct answer is 25 minutes (not among the options provided).
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