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Interesting problem

  1. Dec 14, 2009 #1
    There is a popular myth that after drinking a bottle of water, the last bit is mostly backwash. Well I decided to try and test it, but got stumped.

    Lets call y the amount of backwash in the bottle
    Lets call x the number of sips taken
    The volume of the bottle will be 1000mL
    Assume each sip is 20mL
    Assume that each sip backwashes 0.05mL into the bottle

    dy/dx= 0.05 -20( y / (1000 -(20-0.05) x ) )

    I can't separate variables here, so I do not know what to do. This is not a homework problem, I was just wondering if anyone could help me solve this differential equation. At 51 sips there will be nothing left in the bottle.
  2. jcsd
  3. Dec 14, 2009 #2


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    Homework Helper

    I tinkered with it a bit... try making the change of variables [itex]x' = 1000 - (20 - 0.05)x[/itex], then look at http://en.wikibooks.org/wiki/Differential_Equations/Exact_1 [Broken]. I didn't take the calculation all the way through but it looks solvable that way.
    Last edited by a moderator: May 4, 2017
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