A 2-lane highway is to be constructed across a 6-ft diameter metal culvert which is oriented perpendicular to the highway center line. The culvert is located at station 33+00, and the invert (bottom) of the culvert has an elevation of 150 ft. The elevation of station 21+00 on the tangent alignment is 140 ft. The alignment gradient is +4.0% from station 21+00 to station 29+00, and the gradient from station 29+00 to 37+00 is -3%.

a. Find the longest full station vertical curve that will give approximately 3 ft (3 plusminus 0.5 ft) of cover over the top of the culvert.
b. Compute the station and elevation of the PVC and PVT and the elevation of each full station on the vertical curve.