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July 9th, 2014, 03:41 AM  #1 
Member Joined: Jun 2014 From: Brighton Posts: 49 Thanks: 2  A problem on pipe and tank
Help required to solve my math homework problem A pipe can fill a tank in 5 hours,but because of the leak it takes 5 and half hours to fill the tank.Suppose the tank is full then how much the leak will take to empty the the whole tank? Thanks 
July 9th, 2014, 03:34 PM  #2 
Newbie Joined: Jul 2014 From: Arizona Posts: 20 Thanks: 0 
It would take 50 hours for the leak to empty the whole tank. The reasoning behind that is because the pipe fills the tank with liquid in 5 hours, but due to the leak it takes 5.5 hours to fill the tank. So for every 5 hours the pipe leaks half an hour(.5) worth of liquid. 5 hours  .5 leaked 10 hours  1 15h  1.5 20h  2 25h  2.5 & 50h  5 
July 9th, 2014, 04:21 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,112 Thanks: 1002 
55 hours.

July 9th, 2014, 05:33 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond 
$\displaystyle \frac{11}{2}\left(\frac15\frac1L\right)=1\Rightarrow L=55$

July 9th, 2014, 07:14 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,112 Thanks: 1002 
Melikes: u = time to fill tank with no leak (5) v = time to fill tank with leak (5.5) w = time to empty tank due to leak (?) General case: w = uv / (v  u) w = 5(5.5) / (5.5  5) = 55 
July 10th, 2014, 04:53 PM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond 
1/w = 1/u  1/v.

July 11th, 2014, 01:13 AM  #7 
Newbie Joined: Jun 2014 From: United state Posts: 14 Thanks: 0 Math Focus: algebra, geometry, trigonometry, calculus 
w=uv/(vu) u= time to fill tank with no leak v= time to fill tank with leak w= time to empty tank due to leak so w= 5 x 5.5 / (5.55) =55 Thanks for more details you can also take help online tutor. 
July 11th, 2014, 02:48 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,112 Thanks: 1002  
July 18th, 2014, 03:59 AM  #9 
Member Joined: Jun 2014 From: Brighton Posts: 49 Thanks: 2 
Thank you all for your answers

July 21st, 2014, 02:07 AM  #10 
Senior Member Joined: Oct 2013 From: Far far away Posts: 422 Thanks: 18  I don't understand the solutions given in this thread I solved it like this (with help from the solutions given in the thread) Let filling rate without leak = x Let leak rate = y Let volume = V Equation (1) V/x = 5 Equation (2) V/(x  y) = 5.5 Using the two equations I get y/V = 1/55 Which means V/y = time taken for the leak to empty the tank = 55 Am I correct? Looking at the answers, it seems that this is a type of problem with a formula to solve it. Any clarification will be appreciated. Thanks 

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