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The time taken to fill a pot with a standard pipe is 18 minutes. Three pipes are used...

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The time taken to fill a pot with a standard pipe is 18 minutes. Three pipes are used to fill the pot with the second able to fill at twice the rate of the standard pipe and the third able to fill at thrice the rate. How long does it take to fill the pot.

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A standard pipe fills the pot in 18 minutes. If the volume of the pot is V, the rate at which it is filled is `V/18` . The second pipe fills at twice this rate or `(2*V)/18` and the third fills at thrice the rate of `(3*V)/18` . If all three pumps are used to fill the pot simultaneously, the rate at which it is filled is `V/18 + (2*V)/18 + (3*V)/18` = `(V + 2V +3V)/18` = `V/3`

The time taken to fill the pot is `V/(V/3) = 3`

The pot can be filled in 3 minutes using all the three pipes together.

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