$($c$)$ An egress system involving a transition, which merges two routes $($routes $1$ & $2)$ into one exit route $($route $3)$ as shown in Figure Q$2$b$.$ The widths of routes $1,2$&$3$ are $1\mathrm{.}5m,1\mathrm{.}5m$ and $2m$ respectively. The boundary layer of each exit is $0\mathrm{.}2m$ at each side. If $300$ occupants are evacuating through route $3,$ where the density of crowd is $1\mathrm{.}2$ persons $\frac{?}{m^2},$ estimate the time to complete the evacuation through route $3.$

$(8$ marks$)$

Figure Q$2$b: A schematic plot of an egress system

$3$