Three Brine Tanks: There are three tanks. Initially the rst tankhas 500 gallons of brine
containing twenty pounds of salt, the second tank contains 200gallons of pure water, and
the third tank contains 1000 gallons of brine containing tenpounds of salt. Brine with a
concentration of 1 lb/gal is poured into the rst tank from anoutside source at a rate of
twenty gallons a second. There are also three tubes connectingthe tanks and they allow
fluids to pass as follows: brine is allowed to move from the rsttank to the second tank
through a tube that allows forty gallons a second to passthrough it, brine is allowed to move
from the second tank to the third tank through a tube thatallows forty gallons a second to
pass through it, and brine is allowed to move from the thirdtank to the rst tank through a
tube that allows twenty gallons a second to pass through it.Lastly, twenty gallons a second
are drained from the third tank and removed from the system.Assume salt is uniformly
distributed within each tank due to stirring.
1. First draw a picture of this situation.
2. Create a model that describes the amount of salt in eachtank at time t.
3. Solve the model. You will need to look at section 5.6 tolearn how to deal with a
nonhomogeneous linear system.
4. Plot your solutions on the same graph (you should havethree equations that you plot
against time t).
5. When does the concentration of the salt in the second tankreach 0:5 pounds a gallon?
6. What quantity of salt will each tank be nearing as t getslarge? How could we have
known this without even building a model?