# [SOLVED] Application Differential Equation: mixture problem.

• Apr 25th 2010, 10:08 PM
Latszer
[SOLVED] Application Differential Equation: mixture problem.
An aquarium pool has volume 2 http://www.webassign.net/images/multiply.gif 10^6 liters. The pool initially contains pure fresh water. At t = 0 minutes, water containing 10 grams/liter of salt is poured into the pool at a rate of 60 liters/minute. The salt water instantly mixes with the fresh water, and the excess mixture is drained out of the pool at the same rate (60 liters/minute).

I need to figure out how to "Write a differential equation for S(t), the mass of salt in the pool at time t."

Any help is appreciated.
• Apr 26th 2010, 01:26 AM
mr fantastic
Quote:

Originally Posted by Latszer
An aquarium pool has volume 2 http://www.webassign.net/images/multiply.gif 106 liters. The pool initially contains pure fresh water. At t = 0 minutes, water containing 10 grams/liter of salt is poured into the pool at a rate of 60 liters/minute. The salt water instantly mixes with the fresh water, and the excess mixture is drained out of the pool at the same rate (60 liters/minute).

I need to figure out how to "Write a differential equation for S(t), the mass of salt in the pool at time t."

Any help is appreciated.

Rate of salt in = (10)(60) = 600 gram/min.

Rate of salt out = (C)(60) = (S/212)(60) = 15S/53 gram/min,

where C is the concentration of salt in the tank at time t.

Therefore ....
• Apr 26th 2010, 01:28 PM
Latszer
dS/dt should be in-out so...

600-3S/100000

EDIT: ok nm...that was 10^6 not 106.

Sorry about posting in calculus, I am still in calculus II and forgot I should post this in the DE section (we are doing DE for the last two weeks of class).
• Apr 26th 2010, 01:35 PM
Latszer
I got the equation S(t) to be S = Aexp(3t/100000), if the pool is fresh initially would A jsut be 1?
• Apr 26th 2010, 03:07 PM
Latszer
I got it...