An intersection operates on a two$-$phase signal. Field measurement shows that start$-$up lost

time is $4$ seconds and clearance lost time is $2$ seconds in each phase. In addition, when

vehicles travel through the intersection at full speed, their saturation headway is $3$ seconds

per vehicle. Traffic demand is given as shown in the figure. Assume volume to capacity ratio

$x=0\mathrm{.}9.$ In addition, approach speed is $20mph$ on $E-W$ street $(50ft$ wide$)$ and $25mph$ in $N-S$

street $(60$ ft wide$),$ the intersection is on level terrain, and vehicle effective length $15ft.$

$(1).$ Find the practical cycle length that is able to accommodate the traffic demand.

$(2).$ Determine phase splits for each phase.