Question $3$: $35$ pts $($Traffic Stream Parameters$)$

While working with loop detector records for a study, you notice that equipment always says $18\%$ of the road is occupied by vehicles regardless of the vehicle counts. To verify this, you decide to take speed measurements using a radar gun at the relevant location. During a $5-$ minute period, you observe $40$ vehicles traveling at $28m\frac{i}{h},50$ vehicles at $32m\frac{i}{h},$ and $30$ vehicles at $35m\frac{i}{h}.$ The typical vehicle length is about $18$ ft $,$ and the loop detector spans $12$ ft $.$

Calculate the traffic density based on your observation. $(15$ pts$)$

Calculate the traffic density according to the loop detector. Compare the observed density with the density from the loop detector data. Do you think the equipment's data is reliable? $(10$ pts $)($Hint: for a loop detector, $k=\frac{\%of\text{r}\text{o}\text{a}\text{d}\text{o}\text{c}\text{c}\text{u}\text{p}\text{i}\text{e}\text{d}by\text{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}\text{s}}{\text{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}\text{l}\text{e}\text{n}\text{g}\text{t}\text{h}+\text{l}\text{o}\text{o}\text{p}\text{d}\text{e}\text{t}\text{e}\text{c}\text{t}\text{o}\text{r}\text{s}\text{p}\text{a}\text{n}\text{s}})$

Calculate the flow rate $($vehicles per hour$)$ observed during the $5-$mintue period. $(5$pts$)$

Calculate how much time each vehicle occupies the detector $(5$pts$)$