# tank modeling problelm for first order ode

• Oct 2nd 2011, 04:04 PM
junwagh
tank modeling problelm for first order ode
Beer containing 6% alcohol per gallon is pumped into a vat that initially contains 400 gallons of beer at 3% alcohol.
The rate at which the beer is pumped in is 3 gallons per minute, whereas the mixed liquid is pumped out at a rate of
4 gallons per minute. (a) Find the number of gallons of alcohol A(t) in the tank at any time t. (b) What is the
percentage of alcohol in the tank after one hour? (c) When is the tank empty?

dy/dt = .06*3 - y(t)/(400-t)

Is this the correct way to set up the problem? What is the relevance of the initial concentration of the beer in the vat? Does that not factor into the problem?
• Oct 3rd 2011, 02:46 AM
tom@ballooncalculus
Re: tank modeling problelm for first order ode
Quote:

Originally Posted by junwagh
dy/dt = .06*3 - y(t)/(400-t)

Is this the correct way to set up the problem?

Except, where is the rate of pumping out? (And why not stick with A, not y?)

Quote:

Originally Posted by junwagh
What is the relevance of the initial concentration of the beer in the vat? Does that not factor into the problem?

That's an initial condition to plug in after solving.