A crest vertical curve is to be designed to join a +4% grade…

A crest vertical curve is to be designed to join a +4% grade with a -1% grade at a section of a two-lane highway. Determine the minimum length of the curve if the design speed of the highway is 70 mph, S < L, and a perception reaction time of 2.5 sec.  The deceleration rate for braking is 11.2 ft/sec2. (Please show all work as best as possible and type out anything that you would like to clearly articulate)