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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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?
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.
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
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.Quote:
Originally Posted by hisajesh
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 writeQuote:
Originally Posted by HallsofIvy
7/144t + (24-t)/36 = 1