So ferry can only arrive/depart Bunk Island on these intervals.
Ferry runs from 8 a.m. to 8 p.m. (t = 5 to 17)
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d)
The earliest ferry can arrive at Bunk Island is at t = 7.87503
It takes 50 minutes (5/6 hour) to get from Main Beach to Bunk Island
Earliest ferry can leave Main Beach is at t = 7.87503 - 5/6 = 7.0417
Time: 3 a.m. + 7.0417 = 3 a.m. + 7 hr 3 min = 10:03 a.m.
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e)
i)
The latest ferry can leave Bunk Island is at t = 16.12497
It takes 50 minutes to get from Main Beach to Bunk Island, and another 5 minutes before ferry leaves Bunk Island again, for a total of 55 minutes = 11/12 hr
Earliest ferry can leave Main Beach is at t = 16.12497 - 11/12 = 15.208303333
Time: 3 a.m. + 15.208303333 = 3 a.m. + 15 hrs 12 min = 6:12 p.m.
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ii)
Note that earliest and latest possible trips all arrive and leave Bunk Island within time interval [7.87503, 16.12497], where depth of water is always at least 2m. So we don't have to worry about tide going out and ferry having to wait for tide to come back in.
It takes 50 minutes to travel in each direction, plus ship spends minimum 5 minutes at each end. So ferry can leave Main Beach every 110 minutes.
Earliest ferry can leave is 10:03 a.m., latest ferry can leave is 6:12 p.m.
Assuming it spends no more than 5 minutes at each end, then ferry can leave Main Beach at following times:
10:03 a.m.
11:53 a.m.
1:43 p.m.
3:33 p.m.
5:13 p.m.
(The next trip would be at 7:03 p.m., which is too late)
Maximum round trips: 5
Mαthmφm