# Working together, it takes two different sized hoses 20 minutes to fill a small swimming pool. If it takes 25 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?

Nov 23, 2016

100 minutes

#### Explanation:

Let whole part of swimming pool = 1,
Two different sized hoses take 20 minutes to fill the whole pool.
So In 1 minute they will fill 1/20 th of the swimming pool.

But the larger hose alone takes 25 minutes to fill the swimming pool.
So In 1 minute it will fill 1/25 th of the swimming pool.

Therefore the smaller hose will fill in 1 minute = $\frac{1}{20} - \frac{1}{25} = \frac{5 - 4}{100} = \frac{1}{100}$ part.

So,The whole part(swimming pool) will be filled by smaller hose = $1 \div \frac{1}{100} = 1 \cdot \frac{100}{1} = 100$ minutes