Math forum

 Water tank problem Options
johan
 #1 Posted : Friday, April 08, 2011 11:04:52 AM

Joined: 1/26/2011
Posts: 22

Water flows into a tank at a rate of 1 gallon per second. Water leaves the tank at a rate of 1 gallon per second for each 100 gallons in the tank. The tank is initially empty. How long will it take for the tank to fill with 50 gallons of water?

Slinger17
 #2 Posted : Friday, April 08, 2011 11:31:04 AM
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Joined: 3/23/2011
Posts: 5

37.5 Seconds methinks

integral of (1 - x/100) from 0 - 50 = 37.5

Slinger17
 #3 Posted : Sunday, April 10, 2011 12:28:43 PM
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Posts: 5

Wait, if there was no leak, it would take 50 seconds, which means the answer must me greater than 50. lolme

tt4lif
 #4 Posted : Tuesday, May 31, 2011 10:36:07 PM
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it is 50  seconds because it on ly takes i second per gallon that flows out!!!! SMARTS

Gyanesh Kumar Verma
 #5 Posted : Friday, May 11, 2012 9:40:26 AM
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Joined: 5/10/2012
Posts: 7

the ovarall rate with which water is being stored in the tank is

dv/dt = 1 - v/100   where v is the volume of the water at a particular time

dv/(1-v/100)=dt

integarting both side ant putting limit from 0 to 50

it results 30.10 seconds

i have another maethod also to derive this result by series and sequences and limits...

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