pipes and cistern problem.

Pipes A and B can fill a cistern in 20 and 30 minutes and C can empty it in 15 minutes.

If the three are opened and closed one after the other successively for 1 min each in that order, how soon will the cistern be filled?

My answer is 180 min but the books answer is 167 minutes, kindly help.

Re: pipes and cistern problem.

I would look at one 3 minute cycle:

minute 1: A is open, B is closed, C is closed. Thus 1/20 of the cistern is filled.

minute 2: A is closed, B is open, C is closed. Thus 1/30 of the cistern is filled.

minute 3: A is closed, B is closed, C is open. Thus 1/15 of the cistern is drained.

During this cycle, we have a net increase of 1/20 + 1/30 - 1/15 = 1/60

After the 55th cycle we have 11/12 of the cistern filled, so we only need an additional 2 minutes of the next cycle to fill it for a total of 167 minutes.

Re: pipes and cistern problem.

I wanted to post to let you know I was also tricked by the problem at first, and revised my reply above.

Re: pipes and cistern problem.

Wow, got it! Thanks again!

Re: pipes and cistern problem.

Whew! I was afraid you had left, thinking the book was wrong! I apologize and I am glad you came back to see the correct reasoning! :D

Re: pipes and cistern problem.

:D I was relieved that someone supported my answer but super excited to understand the trick, math and nature are great!