Question

A tank containing 100 gallons of fresh water, julie was supposed to add 10 lb of salt but accidentally added 20 lb. to correct her mistake she started adding fresh water at a rate of 3 gal/min while drawing off salt solution from the tank at the same rate. How long will it take until the tank contains the correct amount of salt?

Answer 1

thus far I know,

\[\frac{dq}{dt}=Rate_{In}-Rate_{out}\]

and rate is

\[Rate=Concentration*Flow\],

Resulting in units of

\[\frac{pounds}{\min}\]

Answer 2

At any given instant, the tank contain m lbs of salt (ie concentration = m/100 lb/ga).

Salt balance:

dm/dt = 0 - 3m/100

dm /m = -3/100 dt

Initally (t=0), m = 20


ln(m) - ln(20) = -3/100 * t

m = 10 when t = T

-3/100 * T = ln(10) - ln(20)

T = 100/3 * ln(2) minutes

Answer 3

Holy crap that was fast...Thanks!

Answer 4

You're welcome!! Xo!