A river has a trapezoidal shape with a bottom width of $10$ m and side slopes of $3$:$1($H:L$).$ The $7$Q$10$ flow in the river is estimated as $9\mathrm{.}5$ m $3/$s$,$ Manning$$s n is estimated to be $0\mathrm{.}023,$ and tracer experiments in the river have indicated that the Koussis and Rodriguez$-$Mirasol formulation describes longitudinal dispersion. A factory proposes to discharge industrial wastewater at a rate of $2\mathrm{.}5$ m$3/$s containing a contaminant that has a first$-$order decay rate constant of $3$ h$-1,$ the water$-$quality standard for this contaminant is $5$ mg$/$L$,$ and this standard must be met on the boundary of a mixing zone that is located $100$ m downstream of the discharge location. Hydraulic analysis of the channel flow indicates that depth$-$of$-$flow in the middle of the channel under combined flow $($waste $+$ river$)$ is $1\mathrm{.}8$ m$.$