5 A council wants to convert all of the street lighting in a village to use LED lighting.
The network below shows each street in the village. Each node represents a junction and the weight of each arc represents the length, in metres, of the street.
The street lights are only positioned on one side of each street in the village.
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The total length of all of the streets in the village is 2250 metres.
In order to determine the total number of street lights in the village, a council worker is required to walk along every street in the village at least once, starting and finishing at the same junction.
The shortest possible distance the council worker can walk in order to determine the total number of street lights in the village is \(x\) metres.
5
- Find the value of \(x\)
Fully justify your answer.
[0pt]
[4 marks]
5 - A new council regulation requires that the mean distance along a street between adjacent LED street lights in a village be less than 25 metres.
The council worker counted 91 different street lights on their journey around the village.
Determine whether or not the village will meet the new council regulation.