BMAT 2014 · Question 33 · Optimisation
SaveThe diagram below represents all the ferry routes between the islands in the Kuusi group.Each ferry runs a shuttle service between two islands. The journeys between the main central island (Nolla) and each of the outer islands take 30 minutes in either direction and all journeys between two of the outer islands take 45 minutes. All journeys on each route and in both directions start at 6 am and no journey starts at or after 9 pm: Start times for routes between Nolla and the outer islands: 6:00 6:45 7:30 8:15 9:00 etc. repeating every 3 hours Start times for routes between the outer islands: 6:00 7:00 8:00 9:00 etc. It takes between 5 and 10 minutes to walk between ferry docking points on all the islands.

What is the longest time it could take from Kaksi to Nelja by the most direct route, assuming the next available ferry that same day is always taken?