Question

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

Answer 1

Let the larger pipe fills $x$ part of tank in $1$ hour

the smaller pipe fills $y$ part of tank in $1$ hour

Volume of tank be $V$

From the conditions

$12x+12y=V$

$4x+9y=\frac{V}{2}$

$⟹x=\frac{V}{20},y=\frac{V}{30}$

Time taken by larger pipe to fill the tank is $\frac{V}{x}=\frac{V}{\frac{V}{20}}=20hrs$

Time taken by smaller pipe to fill the tank is $\frac{V}{y}=\frac{V}{\frac{V}{30}}=30hrs$