All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
A Keg of Wine (Posted on 2004-07-14) Difficulty: 3 of 5
A man had a 10-gallon keg full of wine, and an empty jug. On Monday he drew off a jugful of wine and filled up the keg with water. On Friday, after the wine and water had been thorougly mixed, he drew off another jugful and again filled up the keg with water. The keg then contained equal quantities of wine and water.

What was the capacity of the jug?

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
general exact solution | Comment 25 of 27 |
if you want to know the capacity of the jug required toe bring the keg down to a 50/50 mix after n draw/refills then you can find that compacity like this

if x is the capacity of the jug then the amount of wine in the keg after the kth draw and refill is given by
10(1-(x/10))^k
now after the nth draw we want this to be equal to 5 thus
10(1-(x/10))^n=5
(1-(x/10))^n=1/2
1-(x/10)=+-(1/2)^(1/n)
x/10=1-(1/2)^(1/n)
x=10(1-(1/2)^(1/n))

thus putting in various values of n we get

<table x:str="" style="border-collapse: collapse; width: 99pt;" border="0" cellpadding="0" cellspacing="0" width="132"><col style="width: 48pt;" width="64"> <col style="width: 51pt;" width="68"> <tbody><tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt; width: 48pt;" height="17" width="64">n</td> <td class="xl22" style="width: 51pt;" width="68">x</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">1</td> <td class="xl22" x:num="" x:fmla="=10*(1-(1/2)^(1/A2))">5</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">2</td> <td class="xl22" x:num="2.9289321881345245" x:fmla="=10*(1-(1/2)^(1/A3))">2.9289322</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">3</td> <td class="xl22" x:num="2.0629947401590023" x:fmla="=10*(1-(1/2)^(1/A4))">2.0629947</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">4</td> <td class="xl22" x:num="1.591035847462855" x:fmla="=10*(1-(1/2)^(1/A5))">1.5910358</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">5</td> <td class="xl22" x:num="1.2944943670387588" x:fmla="=10*(1-(1/2)^(1/A6))">1.2944944</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">6</td> <td class="xl22" x:num="1.0910128185966073" x:fmla="=10*(1-(1/2)^(1/A7))">1.0910128</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">7</td> <td class="xl22" x:num="0.94276335736093286" x:fmla="=10*(1-(1/2)^(1/A8))">0.9427634</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">8</td> <td class="xl22" x:num="0.82995956795328785" x:fmla="=10*(1-(1/2)^(1/A9))">0.8299596</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">9</td> <td class="xl22" x:num="0.74125287712709542" x:fmla="=10*(1-(1/2)^(1/A10))">0.7412529</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl22" style="height: 12.75pt;" x:num="" height="17">10</td> <td class="xl22" x:num="0.6696700846319259" x:fmla="=10*(1-(1/2)^(1/A11))">0.6696701</td> </tr> </tbody></table>


  Posted by Daniel on 2006-07-09 15:22:58
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information