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Extra Credits $(10$ points$)$

Two vertical curves are designed to connect the end of a tunnel to a bridge as shown. The first curve $($on the left$)$ is a sag, and its PVC is set at the end of the tunnel floor $($elevation $=1500$ ft $).$ It connects to a crest vertical curve $($on the right$).$ This crest vertical curve ends where the bridge deck begins at an elevation of $1540ft.$ Both the tunnel and the bridge have a flat grade. The horizontal distance between the end of tunnel and the start of bridge is $1200$ ft $.$

Determine $(1)$ the highest design speed and $(2)$ curve length and curvature for each vertical curve.