Now Cathy is three times as old as Katie. In six years Cathy will be only twice as old as Katie. How old is each girl now?
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Salt flows in at a rate of (5 g/L)*(3 L/min) = 15 g/min.
Salt flows out at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.
So the net flow rate of salt, given by in grams, is governed by the differential equation,
which is linear. Move the term to the right side, then multiply both sides by
:
Integrate both sides, then solve for :
Since the tank starts with 5 g of salt at time , we have
The time it takes for the tank to hold 20 g of salt is such that