Question

a tank initially contains 200 gal of brine in which 50 lb of salt are dissolved. a brine containing 5 lb/gal of salt runs into the tank at the rate of 3 gal/min. the mixture is kept uniform by stirring and flows out of the tank at the rate of 2 gal/min. let y represent the amount of salt at time t. complete parts a through e.
a at what rate (pounds per minute) does salt enter the tank at time t?
15 lb/min
b what is the volume of brine in the tank at time t?
(200 + t) gal
c at what rate (pounds per minute) does salt leave the tank at time t?
lb/min

Explanation:

Step1: Determine the rate of salt leaving

The rate of salt leaving is given by the formula: Rate of leaving = (Concentration of salt in the tank)×(Rate of outflow).
The concentration of salt in the tank is \(\frac{y}{200 + t}\) (since \(y\) is the amount of salt and volume is \(200 + t\) from part b).
The rate of outflow is \(2\) gal/min.
So, Rate of leaving \(=\frac{2y}{200 + t}\) lb/min.

Answer:

\(\frac{2y}{200 + t}\) lb/min