Consider a two-tank brine system shown to the right. Let x1 be the amount of sal
ID: 2980742 • Letter: C
Question
Consider a two-tank brine system shown to the right. Let x1 be the amount of salt in tank 1 and x2 the amount in tank 2. The volume of tank 1 is 100 gal, and that of tank 2 is 50 gal. Initially there are 50 lb of salt in tank 1 and none in tank 2. The input is 10 gal/min of water containing 0. 2 lb of salt per gallon. Transfer 1 is of 20 gal/min from tank 1 to tank 2, and transfer 2 is 10 gal/min from tank 2 to tank 1. The output is 10 gal/min from tank well-mixed, derive the system of equations x'1+2-1/5x1+1/5x2 x'2=1/5x1-2/5x2 modeling the amount of salt in the two tanks. Use the method of elimination to reduce this to a single equation and solve that to find x1 and x2.Explanation / Answer
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