Mixture Salt mixture A tank initially contains 100 gal of

Chapter 9, Problem 13E

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Problem 13E

Mixture Problems

Salt mixture A tank initially contains 100 gal of brine in which 50 lb of salt are dissolved. A brine containing 2 lb gal of salt runs into the tank at the rate of 5 gal/ min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 4 gal/ min.

a. At what rate (pounds per minute) does salt enter the tank at time t ?

b. What is the volume of brine in the tank at time t ?

c. At what rate (pounds per minute) does salt leave the tank at time t ?

d. Write down and solve the initial value problem describing the mixing process.

e. Find the concentration of salt in the tank 25 min after the process starts.