Question $1(10$ points$)$:

The number of vehicles arriving at the upstream of a freeway bottleneck $($free of queues$)$ is

shown in the table below. Based on the numbers given in the table, determine:

$(1)$ Bottleneck capacity in vehicles per hour $($vph$)(4$ points$)$

$(2)$ Downstream measured flow rate in the third time interval $(2$ points$)$

$(3)$ The demand during the third time interval $(2$ points$)$

$(4)$ Queue length at the end of the third and fourth intervals $(2$points$)$