Answer: The speed of the pleasure boats is 8 kilometres per hour
The winner is Louis Kennedy of Oslo, Norway. There were 143 entries.
Worked answer
Walking
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I meet 8 boats while travelling from E to W.
If, as soon as I get to W, I immediately turn round and walk back to E, I shall arrive back at E with the ninth boat to have left W, so the double journey will have taken 8 x ¼ hours, or 2 hours.
Cycling
I meet 6 boats while travelling from E to W.
If, as soon as I get to W, I immediately turn round and cycle back to E, I shall arrive at the same time as the previously-seen fifth boat, so the double journey will have taken me 4 x ¼ hours, or 1 hour.
Suppose the distance from E to W is d kilometres, and suppose I cycle at v kilometres per hour, then
2 = 2d/(v – 6) and 1 = 2d/v
so v = 2v – 12, whence v = 12 and d = 6.
I took 30 minutes to cycle from E to W, and the 11.45 boat took 15 minutes longer to make the journey, so its speed was 6 kilometres/¾, or 8 kilometres per hour.
