Question

It take $12$ 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 for $9$ hours only half the pool can be filled .How long would it take for each pipe to fill the pool separately.

Answer 1

Let the time taken by the first pipe be $x$ hours and the time taken by the second pipe be $y$ hours.

in 1 hour the first pipe can fill it $=\frac{1}{x}$

in 1 hour the second pipe can fill it $=\frac{1}{y}$

$\frac{1}{x}+\frac{1}{y}=\frac{1}{12}$ --------------(1)

$\frac{4}{x}+\frac{9}{y}=\frac{1}{2}$---------------(2)

Consider $\frac{1}{x}$ be $a$ and $\frac{1}{y}$ be $b$.

$a+b=\frac{1}{12}$ -------------(3)

$4a+9b=\frac{1}{2}$ ----------------(4)

Multiplying equation (3) by $4$, we get,

$4a+4b=\frac{1}{3}$ --------------(5)

Now, Equation $\left(4\right)-\left(5\right)$

$5b=\frac{1}{6}$

$b=\frac{1}{30}$

$y=30$.

substituting the value of $y$ in equation in (3) we get

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

$x=20$.

Hence the first pipe would take $20$ hours and the second pipe would take $30$ hours.