My Math Forum A problem on pipe and tank

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 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: 14,597 Thanks: 1038 55 hours. Thanks from aaliyah
 July 9th, 2014, 05:33 PM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond $\displaystyle \frac{11}{2}\left(\frac15-\frac1L\right)=1\Rightarrow L=55$ Thanks from aurel5
 July 9th, 2014, 07:14 PM #5 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 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 Thanks from greg1313 and roketmike
 July 10th, 2014, 04:53 PM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond 1/w = 1/u - 1/v. Thanks from Denis
 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/(v-u) 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 / (5.5-5) =55 Thanks for more details you can also take help online tutor.
July 11th, 2014, 02:48 AM   #8
Math Team

Joined: Oct 2011

Posts: 14,597
Thanks: 1038

Quote:
 Originally Posted by aaliyah Thanks for more details you can also take help online tutor.

 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: 429 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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