Hosers

In 1 hour a large hose can fill 1/36 part., In 1 hour a small hose can fill 1/48 part., 4 large and 8 small hoses in 1 hour can fill :4(1/36) + 8(1/48) = 5/18 part. So it will be full in 1/(18/5) h = 3.6 h or 3 hours 36 minutes.

The way that I used to solve it is the following:

Lets calculate the ratio of water flow between the small hose and the large hose:

In one hour the large hose fill the pool with $x$ liters of water

9 hoses fills the pool in 4 hours

Inversely proportional ratio

Thus 1 large hose fill the pool in $9\times4=36$ hours.

In one hour the small hose fill the pool with $x$ liters of water

6 hoses fills the pool in 8 hours

Inversely proportional ratio

Thus 1 small hose fill the pool in $6\times8=48$ hours.

The ratio between the water flow is:

$\frac{36}{48}=\frac{3}{4}$

Thus 1 small hose is equal as $\frac{3}{4}$ large hoses.

In final situation the 8 small hoses will wo rk as 6 large hoses ( $\frac{3}{4}\times8=6$ ).

In total it is equivalent $6+4=10$ large hoses.

If 1 large hose fill the pool in 36 hours, 10 large hoses will fill in $36\div10=3.6$ hours (inversely proportional).

3.6 hours is equivalent to $\boxed{\text{3 hours and 36 minutes}}$ !