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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.

$30m\frac{i}{h}$

$60m\frac{i}{h}$

$70$ mi$/$h

$50m\frac{i}{h}$