It takes a smaller hose 3 times as long to fill a small swimming pool as it does a larger hose. It takes both hoses working together 15 minutes to fill the swimming pool. How long will it take the smaller hose to fill the pool by itself?

60 minutes.

Step-by-step explanation:

Let t represent time taken by larger hose in minutes to fill the pool.

Part of pool filled by larger hose in one minute would be .

We have been given that it takes a smaller hose 3 times as long to fill a small swimming pool as it does a larger hose, so smaller hose will take minutes to fill the pool.

Part of pool filled by smaller hose in one minute would be .

We are also told that it takes both hoses working together 15 minutes to fill the swimming pool, so part of pool filled by both hoses in one minute would be .

So it will take 20 minutes for the larger hose to fill the pool alone.

Since smaller hose takes 3 times as long to fill a pool, so 3 times 20 would be 60.

Therefore, it will take 60 minutes for the smaller hose to fill the pool alone.