Question

it can take 12 hours to fill the swimming pool using 2 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 can be filled. how long would it take for each pipe to fill the tank separately
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Answer 1

Answer:

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

Step-by-step explanation:

Given:

It can take 12 hours to fill the swimming pool using 2 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 can be filled.

To find:

how long would it take for each pipe to fill the tank separately?

Step 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 $=\frac{1}{y}$

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

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

Step 2

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

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

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

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

$4 a+4 b=\frac{1}{3}$

Step 3

Now, Equation $(4) - (5)$

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

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

$&y=30 .$

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.

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Answer 2

As per the question the given data is two pipes with larger and smaller diameter fills the swimming pool in 4 and 9 hrs respectively.

It took 12 hours to fill the half of the pool by using 2 pipes.

we have to find how long it takes to fill the pool by the pipes separately.

Let time taken by the larger pipe to fill the tank be x and smaller pipe be y.

In 1 hr it takes 1/x for the larger pipe to fill.

In 1 hr it takes 1/y for the smaller pipe to fill.

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

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

let  $\frac{1}{x}$ be m and $\frac{1}{y}$ be n,then

$m+n=\frac{1}{12}$

$4m+9n=\frac{1}{2}$

multiply $m+n=\frac{1}{12}$ by 4 we get,

$4m+4n=\frac{1}{3}$

subtract$4m+4n=\frac{1}{3} from 4m+9n=\frac{1}{2}$ we get,

$5n=\frac{1}{6}$ which is$n=\frac{1}{30}$

then m can be calculated by substituting n in $m+n=\frac{1}{12}$

we get$m+\frac{1}{30} =\frac{1}{12}$

$m=\frac{1}{12} -\frac{1}{30}$

$m=\frac{3}{60}$which is$\frac{1}{20}$

Therefore x is 20 and y is 30.

first pipe takes 20 hours and second pipe takes 30 hours to fill the swimming pool

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