Answer to Question #296913 in Civil and Environmental Engineering for James

Question

A large tank initially contains 220 gal of brine where there is dissolved 35lb of salt. Starting

at time t = 0, a brine containing 3lb of dissolved salt per gallon flows into the tank at the rate of

6gal/min is kept uniform by stirring and the well-stirred mixture simultaneously flows out of the

tank at a slower rate of 3gal/min. How much salt is in the tank at the end of 20 min?

Answer 1

Initial capacity= 220 gal brine and 35lb of salt

Flow in= 6gal/min

Flow out= 3gal/min

After 20 min=?

Amount of gals contained in the tank given the inflow and outflow= 6gal/min-3gal/min

=3gal/min

V(t)= 220+3t

$\frac{dA}{20}$=($\frac{3lbs}{gal}\times\frac{6gal}{min}$ )-($\frac{At lbs}{Vt gal}\times\frac{3gal}{min}$)

= 20min(3gal/min)

=60gal