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8 pipes can fill a tank in 27 minutes. How long will it take to fill the tank if 2 pipes go out of order?

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3 Answers

It always amazes me when tutors bring more complicated terms into a question for no reason.  If you understood all that nonsense you wouldn't need a tutor!

In this question, you have 2 pipes out of commission so forget about them.  You have 6 working pipes out of 8.

That means the only numbers involved are 8, 6, and 27.

The next thing to understand is that if it takes 8 pipes 27 minutes to fill a tank, and some of them go out, the job is going to take longer, right?  That means if you come up with an answer that's less than 27 minutes, you did something wrong.

What's the easiest way to apply the above three numbers to make 27 fractionally bigger?  Multiply it by the fraction 8 over 6.

If you simplify at this point, the arithmetic is easier.  Eight over six is the same as four over three.  How do you multiply something by 4 over 3?  Multiply by 4 (which means double it twice) and then divide by 3.

Your answer will come out to 36 minutes.

If you must, must, must express the steps in a formal way, you can say:

x = ( n / n - r) * m


n = the number of pipes at the start;

r = the number of pipes lost;

m = number of minutes for n pipes;

x = the number of minutes for r pipes,

     And wow, you look smart.

If 8 pipes can fill a tank in 27 minutues, then the total output needed is 8 pipes x 27 minutes = 216 pipe-minutes.

The fewer pipes you have, the longer it will take, but the total pipe-minutes will be the same. For example, if only one pipe were worrking at the same rate, it would take 216 minutes to fill the tank (1 pipe x 216 minutes = 216 pipe-minutes) .

To answer your question, divide 216 pipe-minutes by 6 pipes:

                216 pipe-minutes/ 6 pipes  =  36 minutes


You can use proportion to do the problem.

To finish the job, the number of pipes required is inversely proportional to time, which means the product of the number of pipes and the time is a constant.

So, 6t = 8*27, where t is the time required for 6 pipes.

Solve for t, t = 8*27/6 = 4*9 = 36 min.