$.A+2\%$ grade intersects with a $-1\%$ grade at station $(535+24\mathrm{.}25)$ at an elevation of $300$ ft $.$ If the

design speed is $65m\frac{i}{h},$ determine:

$($a$)$ the stations and elevations of the PVC and PVT

$($b$)$ the elevations and stations at horizontal distances of $65\mathrm{.}25ft,165\mathrm{.}25ft,265\mathrm{.}25ft,365\mathrm{.}25ft,$

$465\mathrm{.}25ft,565\mathrm{.}25ft,$ and $579$ ft from the PVC$.$

$($c$)$ the station and elevation of the highpoint

Note: This is an equal tangent vertical curve, starting with a $+2\%$ grade and ending with a $-1\%$ grade