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? \boxed{} lb/min

Explanation:

Step1: Recall the formula for the rate of salt entering

The rate of salt entering the tank is given by the product of the concentration of salt in the incoming brine and the rate of flow of the incoming brine.

The concentration of salt in the incoming brine is \(5\) lb/gal and the rate of flow of the incoming brine is \(3\) gal/min.

Step2: Calculate the rate of salt entering

Using the formula \( \text{Rate of salt in}=\text{Concentration}\times\text{Flow rate}\), we substitute the values: \(5\times3 = 15\) lb/min.

Answer:

\(15\)