# Pipes and cistern problem. Pleae explain.

• Dec 20th 2012, 08:10 PM
hisajesh
Pipes and cistern problem. Pleae explain.
A and B can fill a cistern in 7.5 minutes and 5 minutes respectively and C can carry off 14 litres per minute. If the cistern is already full and all the three pipes are opened, then it is emptied in 1 hr. How may liters can it hold?
• Dec 20th 2012, 09:13 PM
chiro
Re: Pipes and cistern problem. Pleae explain.
Hey hisajesh.

Can you show us any partial attempts you have tried on this problem? (Hint: It will involve derivatives).
• Dec 20th 2012, 09:19 PM
hisajesh
Re: Pipes and cistern problem. Pleae explain.
I took A and B as one pipe which fills 1/3 of the cistern every minute and you have a pipe C emptying 14 liters per minute. The cistern is already full in the begining.
So I took the computation as 1+(1/3)(x)-14 litres=0
so x=3.5 and the total cistern can have 10.5 liters.

But the book answer is 40. Can you help?
• Dec 21st 2012, 01:55 AM
earboth
Re: Pipes and cistern problem. Pleae explain.
Quote:

Originally Posted by hisajesh
I took A and B as one pipe which fills 1/3 of the cistern every minute <-- that's correct
and you have a pipe C emptying 14 liters per minute. The cistern is already full in the begining.
So I took the computation as 1+(1/3)(x)-14 litres=0
so x=3.5 and the total cistern can have 10.5 liters.

But the book answer is 40. Can you help?

1. Let V be the volume of the cistern.

2. A and B add 1/3 of V to the filled cistern while C take 14 liters per minute from the cistern. After 1 h = 60 min the cistern is empty:

V + (1/3) V* 60 - 14 * 60 = 0

3. Solve for V.
• Dec 26th 2012, 08:50 PM
ibdutt
Re: Pipes and cistern problem. Pleae explain.
Attachment 26368
Quote:

Originally Posted by hisajesh
A and B can fill a cistern in 7.5 minutes and 5 minutes respectively and C can carry off 14 litres per minute. If the cistern is already full and all the three pipes are opened, then it is emptied in 1 hr. How may liters can it hold?