Not been on here for a while, and much more used to answering questions than asking them. Hopefully someone can help me out with this question though.



We consider a simple mixing problem involving one tank from the chemical industry.



A tank contains 1000m^3 of water in which initially 100kg of saly are dissolved. Salty water (brine) runs in at a rate of 10m^3 per minute and each cubic metre contains 5kg of dissolved salt. The mixture in the tank is kept uniform by stirring. Brine runs out at 10m^3 per minute.



a) Letting y(t) be the amount of salt in the tank at time t, write down in words an expression for the time rate of change y'(t) in terms of salt inflow rate and the salt outflow rate. What is the salt inflow rate? What about the salt outflow rate? (Remember y(t) is the amount of salt in the 1000m^3 tank at time t!) Hence write down the differential equation for the amount of salt in the tank.



b) Find the solution of the initial value problem.



Much appreciated to those that can help, and thanks to those that can't help but have taken the time in reading this in an effort to try.