. Aladdin found a cave filled with boxes of gold, measuring 2 inches × 2 inches × 2 inches, and boxes of silver, measuring 1 inc
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Let 
denote the amount of salt in the tank at time 
. We're given that the tank initially holds 
lbs of salt.
The rate at which salt flows in and out of the tank is given by the relation
Find the integrating factor:
Distribute
along both sides of the ODE:
Since, we get
so that the particular solution for is
The tank becomes full when the volume of solution in the tank at time is the same as the total volume of the tank:
at which point the amount of salt in the solution would be
The rate at which salt flows in and out of the tank is given by the relation
Find the integrating factor:
Distribute
Since
so that the particular solution for
The tank becomes full when the volume of solution in the tank at time
at which point the amount of salt in the solution would be