4 The network opposite shows roads connecting 10 villages, \(A , B , \ldots , J\). The time taken to drive along a road is not proportional to the length of the road. The number on each edge shows the average time, in minutes, to drive along each road.
- A commuter wishes to drive from village \(A\) to the railway station at \(J\).
- Use Dijkstra's algorithm, on the diagram opposite, to find the shortest driving time from \(A\) to \(J\).
- State the corresponding route.
- A taxi driver is in village \(D\) at 10.30 am when she receives a radio call asking her to pick up a passenger at village \(A\) and take him to the station at \(J\). Assuming that it takes her 3 minutes to load the passenger and his luggage, at what time should she expect to arrive at the station?
[0pt]
[2 marks]
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