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 4 L/min and from B into A at a rate of 3 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 8 L/min. The (diluted) solution flows out of the system from tank A at 7 L/min and from tank B at 1 L/min. If initially, tank A contains pure water and tank B contains 20 kg of salt, determine the mass of salt in each tank at time t≥0. A B 4 L/min 8 L/min 0.2 kg/L 7 L/min x(t) 100 L x(0) = 0 kg 3 L/min y(t) 100 L y(0) = 20 kg 1 L/min Q

Mathematics For Machine Technology
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ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
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Problem 41AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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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 4 L/min and from B into A at a rate of 3 L/min. The liquid inside each tank is kept well stirred. A brine solution with a
concentration of 0.2 kg/L of salt flows into tank A at a rate of 8 L/min. The (diluted) solution flows out of the system from tank
A at 7 L/min and from tank B at 1 L/min. If initially, tank A contains pure water and tank B contains 20 kg of salt, determine
the mass of salt in each tank at time t≥ 0.
A
B
8 L/min
4 L/min
0.2 kg/L
x(t)
100 L
x(0) 0 kg
y(t)
100 L
y(0) = 20 kg
7 L/min
1 L/min
3 L/min
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 4 L/min and from B into A at a rate of 3 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 8 L/min. The (diluted) solution flows out of the system from tank A at 7 L/min and from tank B at 1 L/min. If initially, tank A contains pure water and tank B contains 20 kg of salt, determine the mass of salt in each tank at time t≥ 0. A B 8 L/min 4 L/min 0.2 kg/L x(t) 100 L x(0) 0 kg y(t) 100 L y(0) = 20 kg 7 L/min 1 L/min 3 L/min What is the solution to the system? x(t) = y(t)=
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