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6 hours 10 minutes. Labelling stations as 1,2,3,4,5,6,7, one needs to construct a time time table for the line. Denoting xx as any hour of day, then trains leaving from station 1 call at all stations (1,2,3,4,5,6,7) at xx:00, xx:10, xx:20, xx:30, xx:40, xx:50, xx+1:00. Likewise the trains travelling in opposite direction have stops starting from station 7 (7,6,5,4,3,2,1) at xx:00, xx:10, xx:20, xx:30, xx:40, xx:50, xx+1:00. Trains leave platform 1 on the half hour (calling 1,4,7 only), with stopping times xx:30, xx+1:00, xx+1:30. And likewise the trains leaving on the half hour from station 7 (calling stations 7,4,1) have times xx:30, xx+1:00, xx+1:30. With these, one can work out all possible combinations of travelling, so that at least 30 minutes stop is had at each station to drink a pint. The feasible stopping orders worth considering are: 1234567, 1234765, 1456732, 1765432, 1235476. One can then apply these to the train timetable. Very much unexpectedly, the most efficient order is 1235476 (where the person starts drinking at station 1 at half past the hour), taking 6 hours 10 minutes. As a worked example of this, suppose they start at station 1 at 10:30am. They drink a pint there and catch the 11:00 train to station 2. They drink a pint there and catch the 12:10 to station 3. They drink a pint there and catch the 13:20 train to station 5. They arrive at 13:40, drink a pint there, and catch the returning 14:20 train to station 4. They arrive 14:30 at station 4, drink a pint there, and catch the 15:00 train to station 7. They arrive station 7 at 15:30, drink a pint there and catch the returning 16:00 train to station 6. They arrive at station 6 at 16:10 and drink their final pint there, finishing at 16:40 and thus taking them a total of 6 hours 10 minutes to complete.