# Mixture Problems

1. Mar 8, 2012

### jzachey

1. The problem statement, all variables and given/known data

A tank contains 1000L of brine with 15 Kg of dissolved salt. Pure water enters the tank at a rate of 10 L/Min. The soultion is kept thoroughtly mixed and drained from the tank at the same rate. How much salt is in the tank(a) after t minutes and (b) after 20 minutes

2. Relevant equations

∫$\frac{dy}{dt}$=(rate in)-(rate out)

3. The attempt at a solution
A.)15e^(-t/200)
B.)12.3 Kg

-------Okay, I knew the answer to this but this isn't what I wanted to ask but I hope it can help you to help me.

Can someone help me find a formula on the ti 83 to give the answers faster?(so I can check) or a program/app that helps with mixture problems? (also known as separable equations used in differential equations in Calculus II)

2. Mar 8, 2012

### Staff: Mentor

I doubt very much that there is something on the TI 83 that would help here, and I consider this to be a good thing. It might be that someone somewhere has a Web site that lets you enter the parameters in a mixture problem, but I have no idea where one might be, and not much interest in looking for one.

The best way to learn to do these problems is, IMO, to sit down with a piece of paper and write down the differential equation that represents the situation, and then solve the differential equation - by hand.

If you had a job in which your sole responsibility was to solve mixture problems all day, day in and day out, then automating this task to speed it up would make sense. But that's not your situation. Your job is to understand how to extract the important information from a word problem, and go through (and understand!) the steps to finding a solution. The key here is understanding, not speed.

My \$.02

3. Mar 8, 2012

### Ray Vickson

Very well said!

RGV

4. Mar 8, 2012

### jzachey

Thank you Mark44, I understand this problem by heart already, but kindly understand it's a bit time consuming on tests, quizzes so forth.often when your on a limited time frame.

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