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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
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Quote:
 Originally Posted by Azzajazz In the time pipe B was on alone, it fills the tank with $\frac{tx}{6}$ litres of water.
How you obtain this equation: $\frac{tx}{6}$?

 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+b-c........>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
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Quote:
 Originally Posted by skipjack However, t = 2/3 is incorrect.
BUT 3/2 is! 1st typo this year

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