Solve ODE Mixture Question: 100 Gal Water Tank

[cue928]

Tank w/ 100 gal pure water. At time = 0, sugar/water mixture with .2 lbs of sugar per gallon enters at 3 gal/ minute. Drain opened at bottom allows sugar solution to leave at 3 gal per minute. Perfect (lol) mixing occurs.

I show the following:
Rate in: .2 x 3 = .6
Rate out: x/100
Volume: 100

dA/dt = .6 - A/100; I get an integrating factor of e^x/100. It asks what will the sugar content be after 20 minutes. I came up with a C value of 19.4. I get 16.##, they get 9.0348. Any idea where I'm going wrong?

 

[tiny-tim]

hi cue928!

Tank w/ 100 gal pure water. At time = 0, sugar/water mixture with .2 lbs of sugar per gallon enters at 3 gal/ minute. Drain opened at bottom allows sugar solution to leave at 3 gal per minute. Perfect (lol) mixing occurs.
…
dA/dt = .6 - A/100

oooh … what happened to the (second) 3 gal per minute?