1) Two tanks, A and B, are connected to each other via two different pipes. Tank

Question

1) Two tanks, A and B, are connected to each other via two different pipes. Tank A has 300 gallons of brine, and tank B has 100 Gallons of Brine. Brine flows from tank A to tank B at a rate of 5 gallons/minute. Brine flows from tank B to tank A at a rate of 5 gallons/minute. Each tank initially contains 50 pounds of salt.

a) Write the system of differential equations modeling the above scenario.

b) Solve the system anyway you'd like. (eigenvalues or Laplace transform)

c) How much salt is in the Tank A after 5 minutes?

2) Write the solution to the following differential equation as a convolution of two functions.

y'-y= ln(t)/(t+1) where y(0)=0

Explanation / Answer

a)lets take flow rate from tank A to B as qadqa/dt=5 qa(t)=300 qa(0)=50

lets take flow rate from tank B to a as qbdqb/dt=5 qb(t)=100 qb(0)=50

b)taking laplace sQ(s)-q(0)=5/s

sQa(s)-50=5/s

sQb(s)-50=5/s

Qb(s)=(5/s^2+50/s)

Qb(t)=5t+50

Qa(t)=5t+50

C)

after 5min salt in tank is =qa=75

qb=75

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