$15$ marks$)$ A horizontal curve for a railroad line has a radius of curve of $500\mathrm{.}00$ meters. If the length of curve is $600$ meters, length of spiral curves are $120\mathrm{.}00$ meters, the equilibrium elevation is $150\mathrm{.}0$ millimeters, the station at tangent spiral $($TS$)$ point is $14+19\mathrm{.}55$ meters and the elevation at both rails at this station is $225\mathrm{.}000$ meters, determine the inner rail and outer rail elevations at station $16+00\mathrm{.}00.$ Assume the segment of this railroad line from tangent spiral $($TS$)$ to SC to CS and to ST has an upgrade of $0\mathrm{.}5\%($stations are $20$ meters