1. A tank contains 500 litres of pure water. Brine with 0.045 kilograms of salt per litre of water enters the tank at a rate of 10 litres per minute. The solution is well-mixed and leaves the tank at a rate of 10 litres per minute. a) Show that gm, the amount of salt (in kilograms) in the tank at time t (in min- utes), satisfies the differential equation d_y _ _1_ 22501; dt _O'45 50 _ 50 ' b) How much salt is present in the tank after t minutes? c) How long will it take for the tank to contain 11.25 kilograms of salt