Suppose a tank with a total capacity of 60 Gallons is currently only half full of a solution of water with 2% bleach concentration. At time t=0 water with a bleach concentration of 7% is pumped in at a rate of 2 gallons per minute. Water is drained from the tank at a rate of 1 gallon per minute. When the tank is full, everything shuts off. What is the amount of bleach in the tank at this time, and what is the concentration?
I don't need it worked out I just want to know if I set this up right. let me know what i need to add or change anything.
dA/dt = (2)(.07)-(1)(A/30+t)
How much bleach is lost in dt?
-C/Vdt
Where C is the current amount of bleach and V is the current volume.
How much bleach is added in dt?
0.07*2*dt
So:
dC/dt = 0.07*2-C/V
And V = 30+t
Describes the amount of bleach in the tank, with the appropriate initial conditions
And you just need it at the time when the tank is full.
eta: I guess your answer is right up to missing parentheses