Two tanks, each holding 50 L of liquid, are connected by pipes with liquid flowi
ID: 3111126 • Letter: T
Question
Two tanks, each holding 50 L of liquid, are connected by pipes with liquid flowing from tank A into tank B at the rate of 4L/min and from tank B into tank A at 1L/min. The liquid inside each tank is kept well stirred. Pure water flows out of tank B at 3L/min. If, initially, tank A contains 2.5 kg of salt and tank B contains no salt (only water), determine the mass of salt in each tank at time t greaterthanorequalto 0. Graph on the same quantities x_1(t) and x_2(t), where x_1(t) is the mass of salt in tank A and x_2(t) is the mass in tank B.Explanation / Answer
consider tank A
it contains x1 in 50 liters so x1/5
rate in
1 l coming from x2 and 3l coming from out so total 4l
which is 4x2/50
rate out
4l is going into x2 from x1 so 4x1/50
x1'(t)=rate in-rate out=(4x2/50)-(4x1/50)
similarly for tank b
rate in
4l from x1 so 4x1/50
rate out
1l into x1 3l going out total 4l so
4x2/50
x2'(t)=(4x1/50)-(4x2/50)
we know salt in tank a is 2.5 kg initialy so x1(0)=2.5
and x2(0)=0 as there is no salt initally
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