Question

it takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool?

Answer 1

Let the pipe with large diameter and smaller diameter be pipes $A$ and $B$ respectively. Also let pipe $A$ work at a rate of $x$ hours/ unit and pipe $B$ work at a rate of $y$ hours/unit. According to the question,
$x+y=\frac{1}{12}\Rightarrow 12x+12y=\mathrm{1.....}\left(i\right)$
and $4x+9y=\frac{1}{2}\Rightarrow 8x+18y-1.....\left(ii\right)$
Multiply (i) by $2$ and (ii) by $3$, we get
$24x+24y-2$ and $24x+54y-3$
on solving we get, $30y=1\Rightarrow y=\frac{1}{30}$
and $x=\frac{1}{20}$
Hence, the pipe with large diameter will take $20$ hours to fill the swimming pool and the pipe with smaller diameter will take $30$ hours to fill the swimming pool.