12. A certain polluted lake holds 50kL of water. Pure water flows into the lake rate of 2kL per hour, and water flows out of the lake at the same rate. The lake is polluted cyanide, the initial concentration of which is 3g per kL. In order to be deemed safe to swim in concentration of cyanide has to decrease to 1g per kL. Assuming instantaneous mixing, how will it be before the water is safe to swim in?

3. A large tank with the capacity of 500 gallons is fully filled with pure water. Brine containing 2 pounds of salt per gallons is pumped into the tank at a rate of 5 gal/min. Find the amount A(t) pounds of salt in the tank at timer minutes, if the well-mixed solution is pumped out (a) with the same rate as the entering one; and (b) with the rate of 10 gal/min. In case (a), how much salt is in the tank after a long time? In case (b), what is the concentration of the solution in the tank by the time it is empty? (c) Let everything be the same except that, initially, the tank is filled with 250 gallons of pure water, while the well-stirred solution is pumped out with the flow rate of 2.5 gal/min. Find (t). What is the concentration of the solution in the tank by the time it is fully filled? Hint: (a) The volume of the solution in the tank at time (b) The volume of the solution in the tank at time minutes is V(t)= 500 gallons minutes is V(t)=500-5r gallons (c) The volume of the solution…

9. A glass container can hold 35 liters of water. It currently has 10 liters of water with 15 grams of Gatorade power initially dissolved in the container. A solution is poured into the container at 3 liters per minute - the solution being poured in has 0.5 grams per liter of Gatorade powder. Assume the solution in the container is well mixed. There is an outflow at the bottom of the container which has liquid leaving at 1 liter per minute. Let G(t) denote the amount of Gatorade powder in the tank at time t. a. Setup the differential equation for G'(x). b. Solve for the general solutiont) c. Use initial condition to find the specific solution. (Write out the entire solution, with the constant(s) plugged in.) ) d. When will the container overflow?

2. A large tank initially contains 100 gallons of brine in which 10 lb of salt is dissolved. Starting at t = 0, pure water flows into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring, and the well-stirred mixture simultaneously flows out at the slower rate of 2 gal/min. a) How much salt is in that tank at the end of 15 min and what is the concentration at that time? b) If the capacity of the tank is 250 gallons, what is the concentration at the instant the tank overflows?