35. Mixing. Suppose a brine containing 0.2kg of salt per liter runs into a tank initially filled with 500L of water containing 5kg of salt. The brine enters the tank at a rate of 5L/min. The mixture, kept uniform by stirring, is flowing out at the rate of 5L/min (see Figure 2.6). Figure 2.6 Mixing problem with equal flow rates (a) Find the concentration, in kilograms per liter, of salt in the tank after 10min. [Hint: Let A denote the number of kilograms of salt in the tank at t minutes after the process begins and use the fact that rate of increase in A= rate of input - rate of exit. A further discussion of mixing problems is given in Section 3.2.] (b) After 10min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank (see Figure 2.7). What will be the concentration, in kilograms per liter, of salt in the tank 20min after the leak develops? [Hint: Use the method discussed in Problems 31 and 32.] Figure 2.7 Mixing problem with unequal flow rates 35. Mixing. Suppose a brine containing 0.2kg of salt per liter runs into a tank initially filled with 500L of water containing 5kg of salt. The brine enters the tank at a rate of 5L/min. The mixture, kept uniform by stirring, is flowing out at the rate of 5L/min (see Figure 2.6). Figure 2.6 Mixing problem with equal flow rates (a) Find the concentration, in kilograms per liter, of salt in the tank after 10min. [Hint: Let A denote the number of kilograms of salt in the tank at t minutes after the process begins and use the fact that rate of increase in A= rate of input - rate of exit. A further discussion of mixing problems is given in Section 3.2.] (b) After 10min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank (see Figure 2.7). What will be the concentration, in kilograms per liter, of salt in the tank 20min after the leak develops? [Hint: Use the method discussed in Problems 31 and 32.] Figure 2.7 Mixing problem with unequal flow rates