Problem $4\mathrm{.}1(10$ Points$)$

A northbound $($NB$)$ freeway is to be designed as a passenger$-$car$-$only facility for an AADT of $35,000$ vpd$.$ It is estimated that the freeway will have a FFS of $70$ mph $.$ The peak$-$hour factor is estimated to be $0\mathrm{.}85$ with $65\backslash \%$ of the peak$-$hour traffic travelling in the peak direction.

Determine the number of lanes required to provide at least a LOS C using the highest annual hourly volume and the $\backslash (30^\{\backslash$text $\{$th $\}\}\backslash )$ highest annual hourly volume.

$($Assume a K factor of $0\mathrm{.}148$ for highest annual hourly volume and a $\backslash (\backslash$mathrm$\{$K$\}\_\{30\}\backslash )$ of $0\mathrm{.}12$ for the $\backslash (30^\{\backslash$text $\{$th $\}\}\backslash )$ highest annual hourly volume$)$

Hint: you will need to perform some trials.