An equal$-$tangent vertical curve is to be constructed between grades of $-2\mathrm{.}0\%($initial$)$ and $+1\mathrm{.}0\%($final$).$ The PVI is at station $110+00$ and at elevation $420$ ft$.$ Due to a street crossing the roadway, the elevation of the roadway at station $112+00$ must be $424\mathrm{.}5$ ft$.$ Design the curve.