a$)$ Design an equal tangent $($symmetrical$)$ vertical curve. Select a design speed of $55$ mph$.$ Determine the curve$$s length based on the sight distance criterion for a vertical curve. Choose the backward and forward tangent grades to be $2\%$ and $-3\%.$

b$)$ Provide the station and elevation of the VPC and VPT$.$ Assume that the station of the VPI is $300+16\mathrm{.}50$ and its elevation $550$ ft$.$