# A chemical mixing tank

Calculus Level pending

At time $$t = 0$$,a tank contains $$Q(0)$$ lb of salt dissolved in 100 gallons of water.Assume that water containing $$\frac{1}{4}$$ lb of salt/gal is entering the tank at the rate of $$r$$ gallon/min and that the well-stirred mixture is draining from the tank at the same rate.

Let $$Q(t)$$ denote the amount of salt in the tank at any time $$t$$ and $$Q(L)$$ denote the amount of salt present after a very long time(infinitely long).

If $$r=3$$ and $$Q(0) = 2*Q(L)$$,find the time T (in minutes) after which the salt level is within $$2$$% of $$Q(L)$$.

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