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

A tank contains 70 kg of salt and 2000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min.

Find the amount of salt in the tank after 2 hours.

I'm failing to figure out how to manipulate the rate-in to include it in a differential equation that models this process.

2. Relevant equations

Q= amount of salt in tank

[tex]\frac{dQ}{dt}= Rate in - Rate out[/tex]

Rate out: [tex]\frac{Q}{2000} \cdot 6(Liters/min)[/tex]

The rate in is 12L/min but of pure water, so I can't just have a simple rate in - rate out as I had envisioned.

3. The attempt at a solution

Realizing the 12L/min is a rate that affects the volume of water, I solved this simple differential equation and put it in my equation for rate out: rather than dividing Q by 2000, I'm dividing it by 12t +2000.

Problem is that this doesn't seem to work. So I need help on figuring out how or where this rate of pure water falls into my differential equation.

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# Homework Help: Modeling with First Order Differential Equation

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