5 A rapid transport system connects 8 stations using three railway lines.
The blue line connects A to B to C to D . The red line connects \(B\) to \(F\) to \(E\) to \(D\). The green line connects E to G to H to A .

• The travel times for the return journeys are the same as for the outward journeys (so, for example, the travel time from B to A is 5 minutes, the same as the time from A to B ).
• All travel times include time spent stopped at stations.
• No trains are delayed so the travel times are all correct.
  1. (i) Model the blue, red and green lines, and the travel times above, as a network.
     (ii) Use Dijkstra's algorithm to find the quickest travel times from C to each of the other stations.
  2. 1. Write down a route from A to D with travel time 12 minutes.
     2. Construct a table of quickest travel times.
  3. Give a reason why the quickest journey from A to D may take longer than 12 minutes.