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# Solution

Okay. We have to find how long it takes the narrow pipe to fill up the tank on its own. Let the time it takes to fill up the tank be "t" minutes.

The wide pipe fills up the tank three times faster; it means it requires one-third the time required by the narrow one. Therefore, the wide pipe on its own fills up the tank in t/3 minutes.

Let's get back to the narrow pipe. Let's suppose the tank holds "L" litres of water. The narrow pipe, therefore, takes "t" minutes to fill "L" litres of water. So, in one minute it will fill up L/t litres of water.

The wide pipe takes t/3 minutes to fill "L" litres of water. So, in one minute it will fill L/(t/3), that is 3L/t litres of water.

Together the two pipes will fill up L/t + 3L/t litres of water in one minute. This means the two pipes together fill up 4L/t litres of water in one minute. In one minute they fill 4L/t litres of water, so in 40 minutes they, together, fill up 40 x 4L/t litres of water, that is 160L/t litres.

But in 40 minutes they, together, fill up the tank; that is, they fill "L" litres of water in 40 minutes. So, 160L/t = L.

So, 160/t = 1, or t = 160. But "t" is the time required by the narrow pipe to fill up the tank on its own. Therefore, the narrow pipe, on its own, fills up the tank in 160 minutes. Did I get it right, or did I make a mistake somewhere?

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