6 A council wants to grit all of the roads on a housing estate. The network shows the roads on a housing estate. Each node represents a junction between two or more roads and the weight of each arc represents the length, in metres, of the road.
\includegraphics[max width=\textwidth, alt={}, center]{5ff6e3bb-6392-49cf-b64d-23bc595cd92e-08_1145_1458_539_292} The total length of all of the roads on the housing estate is 9175 metres.
In order to grit all of the roads, the council requires a gritter truck to travel along each road at least once. The gritter truck starts and finishes at the same junction. 6

1. The gritter truck starts gritting the roads at 7:00 pm and moves with an average speed of 5 metres per second during its journey. Find the earliest time for the gritter truck to have gritted each road at least once and arrived back at the junction it started from, giving your answer to the nearest minute. Fully justify your answer.
   [0pt] [6 marks]

   6	Explain how a refinement to the council's requirement, that the gritter truck must start and finish at the same junction, could reduce the time taken to grit all of the roads at least once. [2 marks] \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\)

   The planning involves producing an activity network for the project, which is shown in Figure 1 below. The duration of each activity is given in weeks. \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{5ff6e3bb-6392-49cf-b64d-23bc595cd92e-10_965_1600_559_221}
   \end{figure}