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Two large tanks, each holding 100L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3L/min and from B into A at a rate of 1L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.1kg/L of salt flows into tank A at a rate of 6L/min. The (diluted) solution flows out of the system from tank A at 4L/min and from tank B at 2L/min. If initially, tank A contains pure water and tank B contains 10kg of salt, determine the mass of salt in each tank at time t≥0. What is the solution to the system? x(t)=
y(t)=

Transcribed Image Text:Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing
from tank A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min. The liquid inside
each tank is kept well stirred. A brine solution with a concentration of 0.1 kg/L of salt flows into
tank A at a rate of 6 L/min. The (diluted) solution flows out of the system from tank A at 4 L/min
and from tank B at 2 L/min. If initially, tank A contains pure water and tank B contains 10 kg
of salt, determine the mass of salt in each tank at time t≥ 0.
A
B
6 L/min
3 L/min
0.1 kg/L-
x(t)
y(t)
100 L
x(0) = 0 kg
100 L
y(0) = 10 kg
4 L/min
1 L/min
What is the solution to the system?
x(t)=
y(t) =
B
2 L/min
☺
☑
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