$(14$ points$)$ During a combined sewer overflow event, discharge from sewer pipes and drainage pipes flows into the river because the sewer is too full. Consider a storm in which the volumetric flowrate in a drainage pipe $($water at $25$C$)$ is $0\mathrm{.}20$ m$3/$s and the volumetric flowrate of sewage $($with a specific gravity of $2\mathrm{.}8)$ is $0\mathrm{.}15$ m$3/$s$.$

a$.(8$ points$)$ If the volume available to fill with both flows before the combined sewer overflow begins is $3,500$ m$3,$ how long in hours will it take for the overflow to start assuming a constant influx of each flow?

b$.(6$ points$)$ Once the overflow has reached steady state, what is the average density of the flow into the river in kg$/$m$3?$