A rectangular lake $300$ m long by $300$ m wide has a uniform depth of $45$ m$,$ which is maintained by an overflow at one end. The other end of the lake connects with a confined aquifer along the whole $300$ m of the side, but nowhere else. The aquifer is horizontal and is $10$ m deep: its porosity is $0\mathrm{.}25$ and its hydraulic conductivity is $3$ m$/$day$.$ The aquifer is fed at its other end, $500$ m away, by another rectangular lake $600$ x $1000$ x $30$m$,$ whose water level is $15$ m above the level of water in the first lake. The lake is in contact with the whole of the aquifer's cross$-$section. An industrial accident causes a chemical toxic to fish to be spilled in the upper lake and rapidly mixed throughout the whole lake, the resulting concentration of $400$ ppm being $80$ times the minimum for fish toxicity. All the fish in the upper lake are killed, with negligible reduction of the toxic chemical's concentration, and the polluted water begins to flow along the aquifer towards the dower lake. pushing the fresh water already there in front of it$.$You are given the task of estimating the minimum time at which the level of toxicity in the lower lake would sturt to kill fish. This means assuming the most unfavourable circumstances and calculating accordingly. What are the most unfavourable circumstances and what is the minimum time associated with them?