(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A tank initially contains 100 gal of brine whose salt concentration is 1/2 lb/gal. Bine whose salt concentration is 2 lb/gal flows into the tank at the rate of 3 gal/min. The mixture flows out at the rate of 2 gal/min. Find the salt content of the brine and its concentration at the end of 30 min.Hint. After 30 min, the tank contains 130 gal of brine.

2. Relevant equations

[tex]\Delta[/tex]x = change in salt content in time interval [tex]\Delta[/tex]t

3. The attempt at a solution

This is the model I have come up with but can't get the correct answer:

[tex]\Delta[/tex]x = 6[tex]\Delta[/tex]t - (2x[tex]\Delta[/tex]t)/(100 + t)

6[tex]\Delta[/tex]t because salt content is increasing this much every interval.

- (2x[tex]\Delta[/tex]t)/(100 + t) because the salt content is decreasing this much every interval. (100 + t) represents that the total amount of gallons of brine are increasing this much every minute because 3 gals are entering and 2 gallons are leaving - hence a net of 1 gal/min increase.

If this is the correct equation, I am having a problem solving the diff. eq.

Thanks

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# Homework Help: Dilution and Accretion Problem - Diff. Eq.

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