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September 10th, 2018, 08:50 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  How to solve this emptying pipe problem?
Pipe A and Pipe B can fill a tank in 12 mins and 6 mins respectively, whereas pipe C can empty it completely in 5 mins B is opened to fill an empty tank After some time, A and C are also opened, after which it takes 15 min to fill the tank. How long was B open alone? "x" is the volume of the tank. Q denotes the flow rate of each respective pipe. Qa = x/12 Qb = x/6 Qc = x/5 After this step, how to proceed ? 
September 10th, 2018, 10:37 PM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
Let $t$ be the amount of time pipe B was open by itself and say the tank can hold $x$ litres. In the time pipe B was on alone, it fills the tank with $\frac{tx}{6}$ litres of water. When pipe A and pipe C are also turned on for 15 minutes, the pipes combined fill the tank with $15(\frac{x}{6} + \frac{x}{12}  \frac{x}{5})$ litres of water. Since the tank is filled up in this time, we can form the equation $$\frac{tx}{6} + 15(\frac{x}{6} + \frac{x}{12}  \frac{x}{5}) = x.$$ Now solve for $t$. 
September 10th, 2018, 11:00 PM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
September 11th, 2018, 02:25 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,109 Thanks: 1909 
As B can fill the tank in 6 mins, B provides x/6 in each minute, and therefore tx/(6 min) l in time t.

September 11th, 2018, 10:20 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,804 Thanks: 971 
Look at it as the job being travelling distance 1: A:@a.................1...................>12 B:@b.................1...................>6 C:@c.................1...................>5 B:@b....>t;(A,B,C)@a+bc........>15 a=1/12, b=1/6, c=1/5 bt + 15(a + b  c) = 1 t/6 + 15(1/12 + 1/6  1/5) = 1 Solve for t : t = 2/3 Same as Azzajazz's downunder way ! 
September 11th, 2018, 12:47 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,109 Thanks: 1909 
However, t = 2/3 is incorrect.

September 11th, 2018, 02:39 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,804 Thanks: 971  

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