Tank a Contains 80 Gallons of Water in Which 20 $x ( t )$

Multiple Choice

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 of the system at the rate of 4 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) $\frac { d x } { d t } = 2 - x / 40 + y / 5 , \frac { d y } { d t } = x / 40 - y / 3 , x ( 0 ) = 20 , y ( 0 ) = 5$
B) $\frac { d x } { d t } = 2 - 3 x / 40 + y / 15 , \frac { d y } { d t } = 3 x / 40 - y / 5 , x ( 0 ) = 20 , y ( 0 ) = 5$
C) $\frac { d x } { d t } = 4 - 3 x / 40 + y / 15 , \frac { d y } { d t } = 3 x / 40 - y / 5 , x ( 0 ) = 20 , y ( 0 ) = 5$
D) $\frac { d x } { d t } = 4 - x / 40 + y / 5 , \frac { d y } { d t } = x / 40 - y / 3 , x ( 0 ) = 20 , y ( 0 ) = 5$
E) $\frac { d x } { d t } = 2 - 3 x / 40 + y / 5 , \frac { d y } { d t } = x / 40 - y / 5 , x ( 0 ) = 20 , y ( 0 ) = 5$