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?

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- Jan 2nd 2013, 08:46 PMhisajeshPipes 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?

- Jan 2nd 2013, 09:35 PMchiroRe: 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. - Jan 3rd 2013, 04:55 AMbjhopperRe: 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 - Jan 3rd 2013, 05:27 AMHallsofIvyRe: Pipes and cistern problem...
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.

- Jan 3rd 2013, 03:58 PMbjhopperRe: Pipes and cistern problem...