MIXING PROBLEM

I'm trying to do it with the method described in this video: https://www.youtube.com/watch?v=6wk9zWa-Fww, but can't seem to get it right...

A tank initially contains 1000 kg of brine containing 10% salt by mass. An inlet stream of brine containing 20% salt by mass flows into the tank at a rate of 20 kg/min. the mixture in the tank is kept uniform by stirring. Brine is removed from the tank via an outlet pipe at a rate of 10 kg/min. Find the amount of salt in the tank at any time t, and the elapsed time when the amount of salt in the tank is 200 kg.

Question

MIXING PROBLEM

I'm trying to do it with the method described in this video: https://www.youtube.com/watch?v=6wk9zWa-Fww, but can't seem to get it right...

A tank initially contains 1000 kg of brine containing 10% salt by mass.  An inlet stream of brine containing 20% salt by mass flows into the tank at a rate of 20 kg/min. the mixture in the tank is kept uniform by stirring. Brine is removed from the tank via an outlet pipe at a rate of 10 kg/min. Find the amount of salt in the tank at any time t, and the elapsed time when the amount of salt in the tank is 200 kg.

dan815 · Answer

ok

dan815 · Answer

What seems to be the problem?

dan815 · Answer

lnitial salt = 100kg
Rate of Inflow = 20 kg/min
Concentration of Inflow=0.2*20 salt/min
Rate of Outflow = 10kg/min
Concentation of Outflow=Ammount of Salt/Volume of Water *10 salt/min

dan815 · Answer

dA/dt= Rate of Salt inflow - Rate of salt outflow
           =4 - A/(1000+10t) * 10

dan815 · Answer

solve the DE, use A(0) = 100 to get the variation parameter. And then you can finally solve for time When A = 200

dan815 · Answer

I realize calling it concentration of outflow and inflow isn't really right xD, That should say rate of salt inflow and outflow, sorry for my English.