Math Question, show all steps please :)?

Question

It takes 24 minutes to completely fill my bathtub and only 8 minutes to drain a full tub. How long will it take to empty a full tub if the water is left on?

Answer 1

in one minute the filling tap fills 1/24 of the tub
in one minute the emptying tap empties=1/8 of the tub
net emptying per minute=1/8-1/24
=3/24-1/24=2/24=1/12 of the tub
time taken to empty with both thetaps on=12 min

Answer 2

You can fill the tub 1/24 full in one minute, but 1/8 will empty in one munute. So 1/8 - 1/24 will actually be the result if the water is on. This is 3/24 - 1/24 or 2/24 or 1/12 per minute. So it will empty in 12 minutes.

Answer 3

Let

1/8x = time to drain the tub

1/24x = time to fill the tub

1 = time to empty the tub if the water was left on

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1/8x - 1/24x = 1

24(1/8x) - 24(1/24x) = 24(1)

3x - x = 24

2x = 24

2x/2 = 24/2

x = 12 Minutes to empty the tub

The answer is x = 12 Minutes to empty the tub

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Check

1/8x - 1/24x = 1

1/8(12) - 1/24(12) = 1

12/8 = 12/24 = 1

1.5 - .5 = 1

1 = 1

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Answer 4

Suppose the pipe supplies m ccs of water each minute. The capacity of the tub is then 24m cc. If it takes 8 minutes to drain off a full tub, then it drains 24m cc/8 min = 3m cc/min. When the tub is full,containing 24 m cc of water, and ,the tap is on, the tub fills at a rate m cc/min and simultaneously drains of at a rate 3m cc/min; i.e., only drains off at a rate 2m cc/min. The to drain off entire 24m cc, it should take 24m cc / 2m cc/min = 12 min.
Is that OK ?

Carry on.

Answer 5

fill at the rate of 1/24min^(-1)
empty at rate of 1/8 min^(-1)

difference=1/8-1/24=3/24-1/24=2/24=1/12
so it will take 12 min

Answer 6

let the volume of bath tub be v....
the rate of filling of bath tub per min =v/24
the rate of drainin of bath tub per min=v/8
the rate of draining =rate of draining- rate of filling

=v/8-v/24
=v/12
there fore water is lost at a rate of v/12 per min ....
hence time taken =volume/rate of volume loss
=v/v/12
=12 min

Answer 7

the ratio between filling:draining is equal to 24:8
which is
3:1
it takes 3 secs to fill wat goes down in 1 sec...the difference between them is 2secs multiply it by 8 thats 12mins...im not good at showing the way but ims ure thats the rite answer

Answer 8

12 minutes (I never show my working)