Problem $3$: An urban watershed has a paved main ditch as shown. Paths from remote points to the ditch are indicated. The details of the subareas are given below. Determine the peak flow at the outlet of the ditch using rational method. The design return period is $20-$year for which the rainfall intensity $($in$/$hr$)$ is given by $\backslash (178/\backslash$left$($t$\_\{$c$\}+16\backslash$right$)\backslash ),$ where $\backslash ($ t$\_\{$c$\}\backslash )$ is the time of concentration in minutes. $[10]$ Hint: Find velocities and travel times for each path. Find the travel times to the outlet based on the four flow paths to the outlet ABDG, CDG$,$ EDG, and FG$.$ The time of concentration $\backslash (\backslash$left$($t$\_\{$c$\}\backslash$right$)\backslash )$ is the max of the four travel times. Based on time of concentration find the rainfall intensity from the IDF equation given. Find runoff coefficient $\backslash ($ C $\backslash )$ for each surface type, and frequency factor for the return period. Find the peak discharge using rational method using $\backslash ($ C$\_\{$f$\}$ i $\backslash$sum C$\_\{$i$\}$ a$\_\{$i$\}\backslash ).$