Tank a Contains 50 Gallons of Water in Which 2 $x ( t )$

question 39

Multiple Choice

Tank A contains 50 gallons of water in which 2 pounds of salt has been dissolved. Tank B contains 30 gallons of water in which 3 pounds of salt has been dissolved. A brine mixture with a concentration of 0.8 pounds of salt per gallon of water is pumped into tank A at the rate of 3 gallons per minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 4 gallons per minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 1 gallonper minute, and the solution from tank B is also pumped out of the system at the rate of 3 gallons per minute. The correct differential equations with initial conditions for the amounts, $x ( t )$ and $y ( t )$ , of salt in tanks A and B, respectively, at time t are

• A) \(\frac { d x } { d t } = 3 - 2 x / 25 + y / 5 , \frac { d y } { d t } = x / 25 - y / 15 , x ( 0 ) = 2 , y ( 0 ) = 3\)
• B) \(\frac { d x } { d t } = 3 - x / 25 + y / 15 , \frac { d y } { d t } = 2 x / 25 - 2 y / 15 , x ( 0 ) = 2 , y ( 0 ) = 3\)
• C) \(\frac { d x } { d t } = 2.4 - 2 x / 25 + y / 30 , \frac { d y } { d t } = 2 x / 25 - 2 y / 15 , x ( 0 ) = 2 , y ( 0 ) = 3\)
• D) \(\frac { d x } { d t } = 2.4 - x / 50 + y / 30 , \frac { d y } { d t } = x / 40 - y / 3 , x ( 0 ) = 2 , y ( 0 ) = 3\)
• E) \(\frac { d x } { d t } = 2.4 - x / 25 + y / 15 , \frac { d y } { d t } = x / 50 - y / 30 , x ( 0 ) = 2 , y ( 0 ) = 3\)

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