Q$1.(50$ Points$)$

An upgrade of $3\%$ meets a downgrade of $2\%$ at station kilometer $19+7309\mathrm{.}13$ and at elevation of $60\mathrm{.}02$ meters. The length of the vertical curve is $109$ meters. Calculate the distance of the highest point on the curve from the start of the curve.

Q$2.(50$ Points$)$

Utility functions for two different modes of travel are given below, along with a table of attributes.

$\backslash$table$[[,$Travel Time $($TT$)($mins$),$Travel Cost $($TC$)($YTL$),$Wait Time $($WT$)($mins$),$Utility$],[$Drive$,15,90,0,U_D$