Please solve with steps. What is the new ODE, where is DS/dt

[18 pts] Finding an unexpected surplus of funds at the end of the fiscal year, the CSU Math Department decides the addition of a 314-gallon fish tank will exude a calming influence on Clayton State math students. They purchase and set up a saltwater tank, complete with little "mathy" fish. Suppose a brine containing 0.2lb of salt per gallon runs into the tank, which is initially filled with 314 gallons of water containing 9 pounds of salt. The brine enters the tank at a rate of 6 gallons per hour. The mixture, kept uniform by stirring, flows out at the rate of 6 gallons/hour. Unfortunately, after ten (10) hours an angry math professor, suffering an existential crisis over whether her Math 1101 students will ever learn how to factor correctly, savagely attacks the tank, which causes an additional 2 gallons per hour of mixture to flow out of the tank through small leaks. As part of your solution process to the following questions, be sure to clearly show the differential equation(s) that model the problem. (Hint do NOT start time over when the attack occurs.) a) Set up a rate of change equation that models the amount of salt in the tank (in pounds) at time t, prior to the leak starting (don't forget initial conditions!) b) How much salt is in the tank at the time the tank springs the leak? c) Write an equation to describe the volume of brine in the tank, V(t). for any time t> 10. d) Set up a rate of change equation that models the amount of salt in the tank for any time t>10. e) What is the concentration of salt in the tank when the department chair finally discovers the damage to the tank, 20 hours after the math professor lost her mind? f) Write the piece-wise defined function that gives the amount of salt, S(t), in the tank at any given time. [18 pts] Finding an unexpected surplus of funds at the end of the fiscal year, the CSU Math Department decides the addition of a 314-gallon fish tank will exude a calming influence on Clayton State math students. They purchase and set up a saltwater tank, complete with little "mathy" fish. Suppose a brine containing 0.2lb of salt per gallon runs into the tank, which is initially filled with 314 gallons of water containing 9 pounds of salt. The brine enters the tank at a rate of 6 gallons per hour. The mixture, kept uniform by stirring, flows out at the rate of 6 gallons/hour. Unfortunately, after ten (10) hours an angry math professor, suffering an existential crisis over whether her Math 1101 students will ever learn how to factor correctly, savagely attacks the tank, which causes an additional 2 gallons per hour of mixture to flow out of the tank through small leaks. As part of your solution process to the following questions, be sure to clearly show the differential equation(s) that model the problem. (Hint do NOT start time over when the attack occurs.) a) Set up a rate of change equation that models the amount of salt in the tank (in pounds) at time t, prior to the leak starting (don't forget initial conditions!) b) How much salt is in the tank at the time the tank springs the leak? c) Write an equation to describe the volume of brine in the tank, V(t). for any time t> 10. d) Set up a rate of change equation that models the amount of salt in the tank for any time t>10. e) What is the concentration of salt in the tank when the department chair finally discovers the damage to the tank, 20 hours after the math professor lost her mind? f) Write the piece-wise defined function that gives the amount of salt, S(t), in the tank at any given time