Math CentralQuandaries & Queries


Question from ramya, a student:

two pipes P and Q would fill a cistern in 30 mins and 40 mins respectively.
both pipes being opened. find when the first pipe be turned off so that the cistern may be just filled in 20 mins.
1. after 10 mins
2. after 15 mins
3. after 20 mins
4. after 25 mins

Hi Ramya. I'll change the numbers and show you how this kind of thing is solved.

Question: Pipe A takes 15 minutes to fill a cistern and pipe B takes 9 minutes to fill it. How long should you open both pipes before shutting off Pipe A if you want to fill it in exactly 7 minutes?

Solution: Pipe A fills 1/15 of a cistern in a minute and pipe B fills 1/9 of a cistern in a minute. The total time is 7 minutes. All of that time we are running Pipe B. Since rate times time equals volume, Pipe B is contributing:

V = (1/9) x 7 = 7/9 of a cistern.

That means Pipe A must provide the other 2/9 of a cistern. Now we solve for time t:

2/9 = (1/15) t

t = 10/3 = 3 1/3 minutes which is 3 minutes and 20 seconds.

Try it with your numbers.

Stephen La Rocque

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