I've been racking my brain and Can't figure part of this question out...

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A tank initially contains 100 gallons of water with 20 lbs of salt dissolved in int. A solution containing 2 lbs of salt per gallon of water is pumped into the tank at a rate of 1 gallon per minute and the well-mixed solution is pumped out of the tank at a rate of 2 gallons per minute.

A) How much salt will be in the tank after 25 mins?

B) When will there be 55 lbs of salt in the tank? [Note: There are two answers]

C) How much salt will be in the tank after 100 minutes?

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I started out with my initial equation

dS/dt = rate in - rate out

dS/dt = (2)(1) - (s/100)(2)

This was rewritten into a linear equation form

S' + (1/50)S = 2

and plugged in as

S = (∫e^{∫1/50 dt}* 2 dt) / (e^{∫1/50 dt})

Some more magic gets me to

S = 100+Ce^{-t/50}

and solving for C using information given in the problem gets me

S=100-80e^{-t/50}

for A its just plug and chug - t=25 and I get S=51.47 lbs.

for B its more plug and chug - S=55 so I get T=28.76 Mins. However I cant find the second answer.

for C its pretty easy - the tank empties at T=100 so it's 0.

I am really stuck on part B. I know there are two answers, because the salt in the tank fills up to a maximum, then the flow of water out begins to overcome the saltwater solution going in, so my salt level in the tank decreases - the whole thing looks like an inverted parabola shape. However my equation doesn't give me this.

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