The amount of salt in the tank at time
, denoted by
, changes over time according to the differential equation,


Multiply both sides by
:

Now the left side can be condensed to the derivative of a product:
![(\mathrm d)/(\mathrm dt)[e^(t/20)A]=0](https://img.qammunity.org/2020/formulas/mathematics/college/8pxbtyhxojk5ga07ykfvwyr60vuflbrjdg.png)
Integrate both sides to get

and solving for
gives

Given that there are 40 pounds of salt at the start, or
, we know
, so that

We want the concentration to fall to 0.1 lb/gal, which means




so it would take about 73.78 minutes, or about 1.23 hours, for the concentration to fall to 0.1 lb/gal.