Two tanks A and B, each of volume V, are filled with water at time t=0. For t > 0, volume v of solution containing mass m of solute flows into tank A per second; mixture flows from tank A to tank B at the same rate and mixture flows away from tank B at the same rate. The differential equations used to model this system are given by:
d(SA)/dt+v/V*SA= m/V
&
d(SB)/dt+v/V*SB= v/V*SA
Where S stands for sigma (concentration of solute) in tank A or B.
Show that the mass of solute in tank B is given by:
mV/v *{1-e^(-vt/V)} - mt*e^(-vt/V)