Question

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?

Answer 1

60 minutes I believe but it might be wrong cause I did it In my head

Answer 2

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:$\frac{1}{t}+\frac{1}{3t}=\frac{1}{30}$
This simplifies to:
$\frac{4}{3t}=\frac{1}{30}$
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.