Am I setting this diff eq up correctly?

[kdinser]

The problem:
A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved. Brine containing .5 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well mixed solution is then pumped out at a rate of 4 gal/min. Find the number of pounds of salt in the tank after 30 minutes.

I've tried this problem 4 times and before I try it again, I want to varifie that I'm setting it correctly.

A=pounds of salt
t=time in minutes

$$\frac{dA}{dt}=3-\frac{4A}{100+2t}$$

Does this look right?

 

[Doc Al]

It looks right to me.

 

[wais]

Your setup for the differential equation looks correct. You have correctly identified the rate of change of salt in the tank as the difference between the rate of salt entering (6 gal/min x 0.5 lbs/gal = 3 lbs/min) and the rate of salt leaving (4 gal/min x A lbs/gal = 4A lbs/min). However, it would be helpful to include the initial condition of A(0) = 10 lbs to complete the problem. Also, make sure to convert the units of time from minutes to hours to match the units of the rate constants. Overall, your approach seems correct and I would encourage you to try the problem again using your setup. Good luck!