Question $3(40$ points$)$: An equal$-$tangent sag vertical curve is to be constructed between grades of $-2\mathrm{.}0\%($initial$)$ and $+1\mathrm{.}0\%($final$).$ The PVI is at station and at elevation $420-ft.$ Due to a bridge crossing the roadway, the elevation of the bridge at station $112+00$ must be $424\mathrm{.}5-ft.$ Design the curve.