In the intersection shown, consider a case in which Alex St$.$ has two lanes in each direction and Olive St$.$ has only one lane in each direction. The saturation headway was found to be $2\mathrm{.}9$ secs$/$veh$.$ If the intersection is to be setup to have a two$-$phase signal cycle with lost times of $3$ secs per phase, answer the following:

What is the absolute minimum cycle length that could be used?

What cycle length would be required to provide for a v$/$c ratio of $0\mathrm{.}90$ during the worst $15$ minutes of the hour if the $PHF=0\mathrm{.}94?$