Q$\mathrm{.}2$

$($a$)$ A dual carriageway section of road with two lanes in each

direction has a free flow speed of $100$ km$/$h and a capacity of $2,050$

veh$/$h$/$lane$.$ Assuming a linear relationship between speed and

density, estimate the average speed and density of traffic flowing

freely in one direction at $850$ veh$/$h$/$lane$.$

$[4$ marks$]$

$($b$)$ One direction of the dual carriageway section described in

Q$\mathrm{.}2($a$)$ is to be reduced to a single lane as a result of a bus priority

scheme. A speed limit of $85$ km$/$h is also to be imposed.

Assuming jam density will not change, estimate the speed of traffic

flowing freely at $1,700$ veh$/$h$.$

$[4$ marks$]$