The rate at which the amount of salt in the tank,
, changes over time is given by the ODE
and we're told that at the start there is no salt in the tank (fresh water), so
. The amount of solution in the tank is given by
, so the tank will overflow once this expression is the same as the total tank volume, i.e.
We find an integrating factor of the form
then distribute this to all terms of the ODE, giving
Since
, we get
so that the amount of salt in the tank is given by
Then once the tank starts to overflow at
, the amount of salt in the tank is