flow rate puzzle

Roadworks have restricted a motorway to a single lane of traffic and you require to advise what speed would give the greatest flow of traffic assuming that
a) all the vehicles travel at the same speed
b) all keep the same distance apart and obey the Highway coade
c) the average length of vehicle is 13feet

speed thinking distance braking distance Total

@ 20 mph 20ft 20 ft 40ft
@30 " 30ft 45ft 75ft
@40" 40ft 80ft 120ft
@50" 50ft 125ft 175ft
@60" 60ft 180ft 240ft
@70" 70ft 245ft 315ft