Results 1 to 5 of 5

Math Help - Pipes and cistern problem...

  1. #1
    Member
    Joined
    Aug 2012
    From
    Utah
    Posts
    88

    Pipes and cistern problem...

    Pipe A can fill a cistern in 36 minutes and B in 48 minutes. If both the pipes are opened together, when should pipe B be closed so that the cistern may be just full in 24 minutes?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,619
    Thanks
    592

    Re: Pipes and cistern problem...

    Hey hisajesh.

    Basically you have a rate where for some volume V0, we have dV/dt = a litres/minute where a*36 = V0 and dV/dt = b litres/minute where b*38 = V0 (same volume).

    Hint: You need to find a value of t where a*24 + b*t = V0 where t < 24. You have information for a and b in terms of V0 listed above.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    909
    Thanks
    27

    Re: Pipes and cistern problem...

    i/36+1/48 = 84/1728 fraction fill per min A and B
    1/48 fract fill per min B alone
    let x min Aand B
    24-x Balone
    84/1728*x + 1/48*(24-x) =1
    Solve for x
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,583
    Thanks
    1418

    Re: Pipes and cistern problem...

    Quote Originally Posted by hisajesh View Post
    Pipe A can fill a cistern in 36 minutes and B in 48 minutes. If both the pipes are opened together, when should pipe B be closed so that the cistern may be just full in 24 minutes?
    Pipe A is running at a rate of 1/36 "cistern pre minute". Pipe B is running at a rate of 1/48 "cistern per minute" so while they are both running they are filling the cistern at (1/36+ 1/48)= 1/(6*6)+ 1/(8*6)= 4/144+ 3/144= 7/144 "cistern per minute". If they both run for t minutes, they will fill 7x/144 of the cistern. If A only runs for 24- t minutes, it will fill another (24- t)/36 so that to fill the entire cistern will be filed in 7t/144+ (24- t)/36= (7t+ 4(24- t))/144= (3t+ 96)/144= t. Solve that equation for t.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    909
    Thanks
    27

    Re: Pipes and cistern problem...

    Quote Originally Posted by HallsofIvy View Post
    Pipe A is running at a rate of 1/36 "cistern pre minute". Pipe B is running at a rate of 1/48 "cistern per minute" so while they are both running they are filling the cistern at (1/36+ 1/48)= 1/(6*6)+ 1/(8*6)= 4/144+ 3/144= 7/144 "cistern per minute". If they both run for t minutes, they will fill 7x/144 of the cistern. If A only runs for 24- t minutes, it will fill another (24- t)/36 so that to fill the entire cistern will be filed in 7t/144+ (24- t)/36= (7t+ 4(24- t))/144= (3t+ 96)/144= t. Solve that equation for t.
    I see that I filled the cistern with B alone rather than A alone Correction requires changing 48 in equation to 36. Your last sentence is confusing and I thiink you meant to write
    7/144t + (24-t)/36 = 1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Pipes and cistern problem. Pleae explain.
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 26th 2012, 08:50 PM
  2. Pipes and reservoir...problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 26th 2012, 06:31 AM
  3. Pipes and cistern..need your answer.
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 21st 2012, 09:34 AM
  4. pipes and cistern problem.
    Posted in the Algebra Forum
    Replies: 5
    Last Post: December 13th 2012, 09:17 PM
  5. Cistern Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 28th 2008, 07:04 PM

Search Tags


/mathhelpforum @mathhelpforum