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- Sep 16th 2007, 11:10 AM #1

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## Dillusion Problem

An automobile cooling system has a capacity of 17qt. Initially, the system contains a mixture of 2 gal of antifreeze and 9 qt of water. Water runs into the system at the rate of 1 gal/min and the homogeneous mixture runs out a petcock at the same rate. How much anti freeze remains in the system after 5 min?

First I converted the units but after that, I don't know how to solve it.

- Sep 16th 2007, 11:34 AM #2

- Sep 16th 2007, 11:41 AM #3

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- Sep 16th 2007, 11:54 AM #4
it is not the concentration of antifreeze/water, it is the concentration of antifreeze.

Concentration of a solute in a solvent

e.g. what is the concentration of salt solution in which we have 2 grams of salt per gallon of water? 2 grams per gallon, of course, not 2 grams per (gallon + 2 grams)

i think what is confusing you here is the fact that the solute and the solvent have the same units, gallons. but it works out if you think about it

- Sep 16th 2007, 12:09 PM #5

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- Sep 16th 2007, 12:11 PM #6

- Sep 16th 2007, 12:21 PM #7

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- Sep 16th 2007, 12:23 PM #8
when you integrate something, you add +C correct, to replace any arbitrary constant that may have been lost in differentiation. you need to do that to the right hand side of your differential equation when you integrate both sides. then solve for it using the initial data

- Sep 16th 2007, 12:39 PM #9

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- Sep 16th 2007, 12:46 PM #10

- Sep 16th 2007, 01:43 PM #11

- Sep 16th 2007, 01:46 PM #12