3 The diagram shows a simplified map of the main streets in a small town.
\includegraphics[max width=\textwidth, alt={}, center]{4db3fbc5-e664-4803-a5f2-05af376d2591-3_531_1127_301_246} Some of the junctions have traffic lights, these junctions are labelled A to F .
There are no traffic lights at junctions X and Y .
The numbers show distances, in km, between junctions. Alex needs to check that the traffic lights at junctions A to F are working correctly.

1. Find a route from A to E that has length 2.8 km . Alex has started to construct a table of shortest distances between junctions A to F.
   \includegraphics[max width=\textwidth, alt={}, center]{4db3fbc5-e664-4803-a5f2-05af376d2591-3_543_1173_1420_246} For example, the shortest route from C to B has length 1.7 km , the shortest route from C to D has length 2.5 km and the shortest route from C to E has length 1.8 km .
2. Complete the copy of the table in the Printed Answer Booklet.
3. Use your table from part (b) to construct a minimum spanning tree for the complete graph on the six vertices A to F .
   • Write down the total length of the minimum spanning tree.
   • List which arcs of the original network correspond to the arcs used in your minimum spanning tree.
   Beth starts from junction B and travels through every junction, including X and Y . Her route has length 5.1 km .
4. Write down the junctions in the order that Beth visited them. Do not draw on your answer from part (c).