Question

One inlet pipe can fill an empty pool in 12 hours, and a drain can empty the pool in 16 hours. How long will it take the pipe to fill the pool if the drain is left open?

Answer 1

48 hours

Explanation:

So one Pipe can fill an empty pool in 12 hours, and a drain can empty the pool in 16 hours.

So let's just say that x is the value for how much the pool was filled, and y is the time taken.

So which means :

X =
`(1)/(12)y` -
`(1)/(16) y`

`(1)/(12)` represents the volume of the tank being filled up in one hour while
`(1)/(16)` represents the volume of the tank being drained in one hour. By subtracting, we get to know the volume of the tank being filled up in one hour.

So, we solve the equation.

To find X, we make the denominator of the two fractions the same.

X =
`(1)/(12)y` -
`(1)/(16) y`

=
`(1(4))/(12(4))y` -
`(1(3))/(16(3))y`

=
`(4)/(48)y` -
`(3)/(48)y`

Then, we subtract.

`(4)/(48)y` -
`(3)/(48)y` =
`(1)/(48)y`

`(1)/(48)` is the volume of the pool that is filled in one hour

Finally, we find the time taken for the pipe to fill the pool.

If one hour fills
`(1)/(48)y` of the pool, then :

1 =
`(1)/(48)y`

y = 48 hours.

So, the time taken for the pipe to fill the pool with the drain left open is 48 hours.

HOPE THIS ANSWER HELPED :)