Question

The san paulo community swimming pool can be filled in 12 hr if water enters through a pipe alone or in 30 hr if water enters through a hose alone. if water is entering through both the pipe and the hose, how long will it take to fill the pool?

Answer 1

Alright, lets gets started.

If water enters through a pipe alone, swimming pool can be filled in 12 hr.

Or say, in 12 hrs, swimming pool can be filled with help of pipe.

It means in 1 hr, the part of swimming pool filled = $\frac{1}{12}$ (For pipe only)

Similarly, with hose only, , in 1 hr, the part of swimming pool filled = $\frac{1}{30}$

So, water is coming from both, pipe and hose , then in 1 hr, the part of pool filled will be = $\frac{1}{12} + \frac{1}{30}$

Suppose in x hrs, with both supplies, pipe and hose, pool is filled.

Means

$\frac{1}{12} + \frac{1}{30} = \frac{1}{x}$

making common denominator

$\frac{30}{360} + \frac{12}{360} = \frac{1}{x}$

$\frac{30 + 12}{360} = \frac{1}{x}$

$\frac{42}{360} = \frac{1}{x}$

Flipping

$\frac{360}{42} = x$

$x = \frac{60}{7}$

Means 8.57 hrs : Answer

Hope it will help :)