Problem #$1-$ Vertical Curve$-$ Finding curve components and design speed.

An equal tangent crest vertical curve connects a $+3\mathrm{.}2\%$ and a $-1\mathrm{.}1\%$ grade. The PVI is at station $98+20.$ Due to drainage consideration, the highest point on the curve is at station $100+79\mathrm{.}35.$ Determine the following.

a$.$ Station of PVC

b$.$ Station of PVT

c$.$ Design Speed

d$.$ Offset to the curve $($to the first tangent$)$ at the highest point

Please type or write your computations legibly and show your answers on a drawing for the curve.