$(5\mathrm{.}5)$ On a specific westbound section of highway, studies show that the speeddensity relationship is

It is known that the capacity is $4200ve\frac{h}{h}$ and the jam density is $210ve\frac{h}{m}i.$ What is the space$-$mean speed of the traffic at capacity, and what is the free$-$flow speed?

$2.(5\mathrm{.}6)$ A section of highway has the following flow$-$density relationship $q=50k-0\mathrm{.}156k^2[$with $q$ in veh$/$h and $k$ in veh$/$mi$].$ What is the capacity of the highway section, the speed at capacity, and the density when the highway is at onequarter of its capacity?

$3.(6\mathrm{.}1)$ A six$-$lane freeway $($three lanes in each direction$)$ currently operates at maximum LOS C conditions. The lanes are $11ft$ wide, the right$-$side shoulder is $4ft$ wide, and there are $2$ ramps within $3$ miles upstream of the segment midpoint and $1$ ramp within $3$ miles downstream of the segment midpoint. The highway is on rolling terrain with $10\%$ heavy vehicles, and the peak$-$hour factor is $0\mathrm{.}90.$ Determine the hourly volume for these conditions.

$4.(6\mathrm{.}5)$ A six$-$lane freeway $($three lanes in each direction$)$ in a scenic area has a measured free$-$flow speed of $55m\frac{i}{h}.$ There are $7\%$ SUTs and $7\%$ TTs in the traffic stream. One upgrade is $5\%$ and $0\mathrm{.}5mi$ long. An analyst has determined that the freeway is operating at capacity on this upgrade during the peak hour. If the peak$-$hour traffic volume is $3900$ vehicles, what value for the peak$-$hour factor was used? $($Hint: use Table $6\mathrm{.}7$ and interpolation to get $E_T).$