$(20$ points$)$ Problem $6.$ An urban freeway is designed for a rolling terrain with $11-$ft lanes, obstructions $2$ ft from the right edge of the traveled pavement, and $1\mathrm{.}5$ interchanges per mile. The traffic stream consists primarily of commuters. A directional weekday peak$-$hour volume of $2,300$ vehicles is observed, with $700$ vehicles arriving in the most congested $15-$min period. The traffic stream has $15\%$ large trucks and buses and no RVs$.$

$(1)$ How many lanes need to be designed for this freeway to serve at a level of service no worse than B$?$

$(2)$ If AADT is estimated to be $35,000$ veh$/$day for this section. What is the ${30}^{th}$ design hour volume? Assume a directional factor of $60\%.$

CAN YOU PLEASE ANSWER #$2$ ONLY.