Suppose we have a tank that initially contains 10 litres of brine in which there is dissolved 1 kg of salt. Brine containing 0.5 kg of dissolved salt per litre is pumped into the tank at a rate of 6 litres/min. The solution is well stirred and pumped out at a slower rate of 3 litres/min.
Suppose we have a tank that initially contains 10 litres of brine in which there is dissolved 1 kg of salt. Brine containing 0.5 kg of dissolved salt per litre is pumped into the tank at a rate of 6 litres/min. The solution is well stirred and pumped out at a slower rate of 3 litres/min.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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Suppose we have a tank that initially contains 10 litres of brine in which there is dissolved
1 kg of salt. Brine containing 0.5 kg of dissolved salt per litre is pumped into the tank
at a rate of 6 litres/min. The solution is well stirred and pumped out at a slower rate
of 3 litres/min.
a) Write down the differential equation that could describe the amount of salt X(t) in
the tank.
b) How much salt is in the tank at any time t > 0? i.e. solve the IVP you have found
in part (a).
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