Dracula likes to keep his blood well mixed, preferring a mixturethat\'s 50% type

Question

Dracula likes to keep his blood well mixed, preferring a mixturethat's 50% type A and 50% type B (as a good mathematician, hedoesn't like type O because an O looks too much like a 0). Forthese purposes he has a mixing vat that contains 200 gallons ofblood. One day, the vat is filled with 80 gallons of type A and 120gallons of type B. He turns on his blood faucet that lets 2 gallonsper minute of pure type A blood into the vat. Since the vat onlyfits 200 gallons, the extra blood (which you can assume iswell-mixed) flows over the sides for his minions to devour later(they're not as picky). How long will it take before the blood isat a mixture that will make Dracula happy?

I got 18.23 minutes, not sure if that is right.

I integrated dB/dt = -B/100 (making it separable) getting120e^(-t/100) with the initial conditions. Is this correct? and howwould it be done with type A blood, dA/dt?

Explanation / Answer

You are correct. I solved:    A'[t] = 2 - 2(A[t]/200) with the initialcondition that A[0]=80. Got the same answer that you did.

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