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 30 minutes to fill the swimming pool. how long will it take the smaller hose to fill the pool by itself?

Let the time taken to fill the pool using the larger hose alone be t minutes.
Then the smaller hose used alone will take 3t minutes to fill the pool.
When the hoses are used together for one minute, 1/30 th of the pool volume will be added. Now we can write the following equation:
This simplifies to:

3t = 120
t = 40 minutes.
Therefore the smaller hose will take 3 * 40 = 120 minutes to fill the hose by itself.
The answer is: 120 minutes or 2 hours.