Vertical Alignment $-$ min. curve length

Problem $1.$ An equal$-$tangent sag vertical curve is designed with the PVC at station $109+00$ and elevation $950$ ft $,$ the PVI at station $110+77$ and elevation $947\mathrm{.}34$ ft $,$ and the low point at station $110+50.$ Determine the design speed of the curve.

Problem $2.$ Due to a cross street, the elevation of a road at station $112+00$ must be $431\mathrm{.}5$ ft $.$ Initial grade $=-2\mathrm{.}0\%,$ final grade $=1\mathrm{.}0\%,$ PVI is at station $)=(420ft.$ Design the curve. $($Curve$-$through$-$a$-$point problem$)$