Math Problem Statement
A brine solution of salt flows at a constant rate of
6
L/min into a large tank that initially held
100
L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of
5
L/min. If the concentration of salt in the brine entering the tank is
0.5
kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach
0.1kg/L?
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
First-order Linear Differential Equations
Mixing Problems
Formulas
dA/dt = 3 - 5A(t)/(100 + t)
Integrating factor: μ(t) = (100 + t)^5
A(t) = (100 + t)/2 - 50 × 100^5/(100 + t)^5
Theorems
Linear First-order Differential Equations
Mixing Problem Dynamics
Suitable Grade Level
College-level Mathematics or Advanced High School Calculus
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