Question

A tank contains 90 kg of salt and 2000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate 13 L/min. Let y be the number of kg of salt in the tank after t minutes. The differential equation for this situation would be: dy dt = y(0) -

Answer 1

is the Foro mixing proplems we me, dy (rate in) - (nate out) у amount of salt in the tank at time t. The water, entering the tank at 10 L/min, has no salt so rate in o Mixed solution leaves the tank at 13 Lim The tonk now of water and gokg salt initially, The concentration of salt att is 2000 L 2000 kg IL Then rate out is y 2000 By kq/min 2000

Now differential equation is, dy 4.13 2000 dt dy У 13 at 2000 Integrate Iny 13t 2000 + c - 13t 2000 = 13t 2000 7 - e e -13t y - Cie 2000 Non y col =go - 13:0 2000 ce 90 - 0 - 13t 2000 Y = goe