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 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 8 L/min. The (diluted) solution flows out of the system from tank A at 5 L/min and from tank B at 3 L/min. If initially, tank A contains pure water and tank contains 10 kg of salt, determine the mass of salt in each tank at time 120. 8 L/min 4 L/min 0.1 kg Q A x(t) 100 L x(0)=0 kg B y(t) 100 L y(0) 10 kg G 3 L/min 5 L/min 1 L/min What is the solution to the system? x(t) = 18 y(t) =

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.6: Solving Problems Involving Quadratic Equations
Problem 1.3E
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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 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 8 L/min. The (diluted) solution flows out of the system from tank A at 5 L/min and from tank B at 3 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.
8 L/min
4 L/min
0.1 kg/L
A
x(t)
100 L
x(0) = 0 kg
B
y(t)
100 L
y(0) = 10 kg
5 L/min
3 L/min
1 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 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 8 L/min. The (diluted) solution flows out of the system from tank A at 5 L/min and from tank B at 3 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. 8 L/min 4 L/min 0.1 kg/L A x(t) 100 L x(0) = 0 kg B y(t) 100 L y(0) = 10 kg 5 L/min 3 L/min 1 L/min What is the solution to the system? x(t) = y(t) =
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