Marks: --/1 Tank A contains 80 gallons of water in which 20 pounds of salt has b

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Marks: --/1 Tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains 30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentration of 0.5 pounds of salt per gallon of water is pumped into Tank A at the rate of 4 gallons per minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons per minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 2 gallons per minute, and the solution from tank B is also pumped out the of the system at the rate of 4 gallons per minute. The correct differential equations with initials conditions for the amounts, x(t) and y(t), of salt in tanks A and B, respectively, at time t are ... Select the correct answer for x(t), y(t), and the initial conditions. You should select three answer choices.

Choose at least one answer. a. dx/dt = 4 - 3x/40 + y/15
b. dy/dt = x/40 - y/3
c. dy/dt = 3x/40 - y/5
d. x(0) = 20, y(0) = 5
e. dx/dt = 2 - x/40 + y/15
f. dx/dt = 2 - 3x/40 + y/15
g. dy/dt = x/40 - y/5
h. x(0) = 5, y(0) = 20 Marks: --/1 Tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains 30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentration of 0.5 pounds of salt per gallon of water is pumped into Tank A at the rate of 4 gallons per minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons per minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 2 gallons per minute, and the solution from tank B is also pumped out the of the system at the rate of 4 gallons per minute. The correct differential equations with initials conditions for the amounts, x(t) and y(t), of salt in tanks A and B, respectively, at time t are ... Select the correct answer for x(t), y(t), and the initial conditions. You should select three answer choices.

Choose at least one answer. a. dx/dt = 4 - 3x/40 + y/15
b. dy/dt = x/40 - y/3
c. dy/dt = 3x/40 - y/5
d. x(0) = 20, y(0) = 5
e. dx/dt = 2 - x/40 + y/15
f. dx/dt = 2 - 3x/40 + y/15
g. dy/dt = x/40 - y/5
h. x(0) = 5, y(0) = 20 Tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains 30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentration of 0.5 pounds of salt per gallon of water is pumped into Tank A at the rate of 4 gallons per minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons per minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 2 gallons per minute, and the solution from tank B is also pumped out the of the system at the rate of 4 gallons per minute. The correct differential equations with initials conditions for the amounts, x(t) and y(t), of salt in tanks A and B, respectively, at time t are ... Select the correct answer for x(t), y(t), and the initial conditions. You should select three answer choices.

Choose at least one answer. a. dx/dt = 4 - 3x/40 + y/15
b. dy/dt = x/40 - y/3
c. dy/dt = 3x/40 - y/5
d. x(0) = 20, y(0) = 5
e. dx/dt = 2 - x/40 + y/15
f. dx/dt = 2 - 3x/40 + y/15
g. dy/dt = x/40 - y/5
h. x(0) = 5, y(0) = 20 Choose at least one answer. a. dx/dt = 4 - 3x/40 + y/15
b. dy/dt = x/40 - y/3
c. dy/dt = 3x/40 - y/5
d. x(0) = 20, y(0) = 5
e. dx/dt = 2 - x/40 + y/15
f. dx/dt = 2 - 3x/40 + y/15
g. dy/dt = x/40 - y/5
h. x(0) = 5, y(0) = 20

Explanation / Answer

correct answer is option (b)

solution:
x(0)=20, y(0)=5


for x:
rate in=(0.5 salt/gallon)*(4 gallon/ min)+(y(t) pounds/30 gallons)*((2 gallon/min)
=2 + y/15

rate out=(x(t) pounds/80 gallons)*((6 gallon/min)
=3*x(t)/40

dQ
dt = (rate in) - (rate out)

dx
dt=(2+ y(t)/15)-(3*x(t)/40)
=2-3x/40+y/15

for y:
rate in=(x(t) pounds/80 gallons)*((6 gallon/min)
=3x/40

rate out=(y(t) pounds/30 gallons)*((4 gallon/min)+(2 gallon/min into tank A))
=y/5

dQ
dt = (rate in) - (rate out)

dy
dt=(3*x(t)/40)-y(t)/5
=3x/40-y/5

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