Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 l of water containing 5 kg 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 5 l/min. (the same conditions as in the previous problem). after 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank.
(a) find the concentration, in kilograms per liter, of salt in the tank after 10 min. [hint: let a denote thenumber 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.
(b) after 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank. what will be the concentration, in kilograms per liter, of salt in the tank 20 min after the leak develops?