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A tank initially contains 150 gal of brine in which 60 lb of salt are dissolved....

A tank initially contains 150 gal of brine in which 60 lb of salt are dissolved. A brine containing 4 ​lb/gal of salt runs into the tank at the rate of 6 ​gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 5 ​gal/min. Let y represent the amount of salt at time t. Complete parts a through f.

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. What is the solution to the initial value​ problem?

f. Find the concentration of salt in the tank 27 min after the process starts.

Thank you in advance. Please show your work and explain.

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