The Ratio of Water to Wine

Date: 10/22/95 at 0:4:6
From: Anonymous
Subject: Ratios

Hi , I need help with this question and I don't know where to 
begin!!.

A cask is filled with 45 gallons of wine . Nine gallons
are removed and the cask is refilled with water. The nine gallons
of the mixture are removed and the cask is refilled with water 
again.

What is the ratio of water to wine in the final mixture?

Date: 10/23/95 at 11:44:35
From: Doctor Ken
Subject: Re: Ratios

Hello!

Here's how I would approach the problem.  You know what the 
mixture is right after you do the first water replacement: there 
are 36 gallons of wine and 9 gallons of water. So what is the 
ratio of wine to water in the flask at that point? It's 36/9 = 
4/1, so assuming a homogenous mixture, in every 5 parts of liquid 
there are 4 parts wine and 1 part water.  So 4/5 of every volume 
that you remove is wine, and the rest is water.

Now you can figure out how much of the stuff you remove in the 
second round is actually wine, and then you can figure out how 
much is left in the cask.

Good luck!

-Doctor Ken,  The Geometry Forum