Question

Can you show all the steps please?

A salt tank contains 50 lbs of salt dissolved in a 300 gallon tank. A brine mixture with a concentration of 2 lbs of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. The mixture is distributed uniformly in the tank and the mixture is drained at the same rate of 3 gallons per minute input rate of brine 3 gal/min constant 300 gal A Set up the equation that describes the quantity of salt Q(t) in the tank as a function of time t. B Solve the separable equation. output rate of brine 3 gal/min FIGURE 1.3.2 Mixing tank

Answer 1

at time t be alts salt let Quantity of any change in the quantity at t is given by da dt = 3(2) 3 alt) Qlo) - 50 { given 300 6- alts dt 100 @' ta 6. 10o The Solution Stoodt t e Too Integrating This is in the from of linear D.E. is giren yg as follows factor (I) = JI. 6tc » alation 6+6 & Letra) Q = 600-550 100 a. (I) = I et too tipo = 6ooe ta Q (0) =50 50 = 600+L c =-550. as time to Q & Goo

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