# D.E mixing problem need help with rate out

## Homework Statement

A large tank initially hold 40 gallons of water. Pure alcohol enters at a rate of 2 Gal/min is well stirred and the mixture leaves at 1gal/min. What will be the concentration when of alcohol when the tank has 80 gallons of fluid in it.

## Homework Equations

q= amount of alcohol
i have dq/dt=rate in -rate out
rate in=2gal/min of OH
it will take 40 mins to fill to 80 gal
and the thing im wandering about is the rate out.
i currently have
rate out=q/(40+2t), but im thinking maybee its q/(40+t)

as for the rest i think im fine its just this outflow rate im not sure on.

jamesrc
Gold Member
Your second guess for the outflow rate appears correct to me, making your differential equation:
$$\frac{dq}{dt}=2-\frac{q}{40+t}$$

Any reason you are not sure that you would like to discuss?

Don't forget that when you are answering the problem they are asking for concentration of alcohol; your state variable q is currently defined as the amount of alcohol in gallons.

well at first i was thinking of using (40+2t) since that was the initial volume + the flow in but then i thought about how the acutal vol change is just t when you account for the out flow.

as far as the concentration goes what i did was set up the D>E for the quanity of OH in the container then just divid q by (40+2t)

thanks for the help i sortof needed that conformation.