SOLUTION: A milk tank can be filled by pip A in 6 hours, by pipe B in 8 hours and by pipe C in 12 hours. how long will it take all three pipes working together to fill the tank?

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Question 448309: A milk tank can be filled by pip A in 6 hours, by pipe B in 8 hours and by pipe C in 12 hours. how long will it take all three pipes working together to fill the tank?
Found 3 solutions by mananth, ikleyn, greenestamps:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Filling the tank 1 job
Pipe I 6 hours
It does 1/ 6 jobs in 1 minute
Pipe II 8 hours
It does 1/ 8 of thejob in 1 minute
Pipe III 12 hours
It does 1/9 of the job in 1 minute

Together they will do 1/ 6+ 1/ 8++1/12
Together they will do 7/24of the job in one hour
So they will take 3 3/7 hours


Answer by ikleyn(53419) About Me  (Show Source):
You can put this solution on YOUR website!
.
A milk tank can be filled by pipe A in 6 hours, by pipe B in 8 hours and by pipe C in 12 hours.
how long will it take all three pipes working together to fill the tank?
~~~~~~~~~~~~~~~~~~~~~~


        Calculations in the post by @mananth are inaccurate; his solution and his answer are incorrect.
        I came to bring a correct/accurate solution in the form as it SHOULD be presented.


First  pipe makes 1/6 of the job per hour.

Second pipe makes 1/8 of the job per hour.

Third  pipe makes 1/12 of the job per hour.


Working together, the three pipes make

    1%2F6 + 1%2F8 + 1%2F12 = 4%2F24 + 3%2F24 + 2%2F24 = %284%2B3%2B2%29%2F24 = 9%2F24 = 3%2F8

of the job per hour.


Hence, it will take  8%2F3 hours,  or  22%2F3 hours, or 2 hours and 40 minutes to fill the tank,
if all three pipes work together.

Solved.


/\/\/\/\/\/\/\/

And my separate notice in the margins of my solution

        I do not think that somebody will fill a milk tank during 12 hours.



Answer by greenestamps(13258) About Me  (Show Source):
You can put this solution on YOUR website!


Tutor @ikleyn has provided a response showing a solution by the method that is usually taught.

Here is a solution using an alternative method.

Consider the least common multiple of the three given times, which is 24 hours.

In 24 hours...
pipe A could fill the tank 24/6 = 4 times;
pipe B could fill the tank 24/8 = 3 times; and
pipe C could fill the tank 24/12 = 2 times

So in 24 hours the three pipes could fill the tank 4+3+2 = 9 times.

That means the number of hours required for the three pipes together to fill the tank one time is 24/9 = 8/3.

ANSWER: 8/3 hours, or 2 2/3 hours