Can someone explain how to setup this differential mixing problem

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SUMMARY

The discussion focuses on setting up a differential equation to model a tank problem where water is added at a rate of 10 gallons per minute and leaks out at a rate of 1/5 gallons per minute for each gallon present in the tank. The key equation derived is dW/dt = 10 - (1/5)W, where W represents the amount of water in the tank. The goal is to determine the minimum capacity of the tank for the process to continue indefinitely, which requires solving the differential equation using Mathematica.

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erica
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Homework Statement


Setup a differential and solve the differential equation using Mathematica: Suppose water is added to a tank at 10 gal/min, but leaks out at the rate of 1/5 gal/min for each gallon in the tank. What is the smallest capacity the tank can have if the process is to continue indefinitely?

Homework Equations


The Attempt at a Solution


I know Q' = rate in - rate out. I'm clueless I have no idea to set this up. all I have are examples of actual mixing problems where something is being mixed like salt. I'm so confused. please help[/B]
 
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Ok, so you have a tank and you're adding water at a rate of 10 gal/min and it's leaking proportional to the amount of water in the tank. Let's call the amount of water in the tank W, and then the rate of change of amount of water with respect to time would be dW/dt.

So what do you know about these?
 
erica said:

Homework Statement


Setup a differential and solve the differential equation using Mathematica: Suppose water is added to a tank at 10 gal/min, but leaks out at the rate of 1/5 gal/min for each gallon in the tank. What is the smallest capacity the tank can have if the process is to continue indefinitely?

Homework Equations


The Attempt at a Solution

[/B]
I know Q' = rate in - rate out. I'm clueless I have no idea to set this up. all I have are examples of actual mixing problems where something is being mixed like salt. I'm so confused. please help
In words, what does Q represent? You know that the rate of flow into the tank is 10 gal/min. How would you represent the rate of outflow?
 

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