
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 10th, 2018, 07:50 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 310 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, 09:37 PM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 688 Thanks: 243 
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, 10:00 PM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  
September 11th, 2018, 01:25 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,541 Thanks: 1750 
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, 09:20 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,129 Thanks: 914 
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, 11:47 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,541 Thanks: 1750 
However, t = 2/3 is incorrect.

September 11th, 2018, 01:39 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,129 Thanks: 914  

Tags 
emptying, pipe, problem, proceed, solve 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
[ASK] Water Pipe  Monox D. IFly  Geometry  3  July 5th, 2018 04:59 PM 
How long would it take with the third pipe alone?  Chikis  Elementary Math  15  October 17th, 2014 08:30 PM 
A problem on pipe and tank  burgess  Elementary Math  9  July 21st, 2014 02:07 AM 
Work emptying/filling a spherical tank  Singularity  Calculus  0  January 9th, 2013 10:54 AM 
Probability of emptying one of the sets  momo  Advanced Statistics  4  August 10th, 2010 11:51 AM 