A water treatment plant consists of $4$ identical units that are essentially CSTRs$,$ each having a residence time of $5$ hours. The operator suddenly discovers that the feed to the first unit is contaminated with a toxic chemical that was dumped into the river from a chemical plant upstream and cannot be removed in the treatment process.

Since she notices it quickly, she is able to switch the water being fed to the unit from the river to a different water source after only a few minutes, so that the addition of the toxic chemical to the first unit could be considered to be a pulse. If the operator wished to $$dump$$ the most contaminated water $($i$.$e$.$ that water which

contains $68\%($roughly one standard deviation$)$ of the contaminant$)$ back into the river, when should she begin and end the dumping action?