# Enigmatic Code

Programming Enigma Puzzles

## Enigma 1521: Boat scenes

New Scientist #2683, 22nd November 2008 [link]

Pleasure boats ply in each direction along the canal from Eastbridge to Westford and back. They leave each place on the hour and every 15 minutes.

One day I left Eastbridge to walk along the towpath to Westford. I left at 12 o’clock and arrived at Westford at the same time as the boat that had left Eastbridge at 12.15. On my walk I saw eight boats going in the opposite direction, including one which arrived at Eastbridge as I left, and one which left Westford as I arrived.

The next day I left Eastbridge to cycle along the towpath to Westford at 6 kilometres per hour faster than I walked. Again, I left at 12 o’clock but this time I arrived at Westford at the same time as the boat which had left Eastbridge at 11.45. On my walk I saw six boats going in the opposite direction, including one which arrived at Eastbridge as I left, and one which left Westford as I arrived.

What is the speed of the boats?

[enigma1521]

### One response to “Enigma 1521: Boat scenes”

1. Jim Randell 14 August 2012 at 9:16 am

I didn’t program this one, as the result was apparent with a little analysis…

I leave Eastbridge at 12:00 and arrive at Westford when the 12:15 boat arrives.

I see 8 boats going in the opposite direction, they will be boats with the following
arrival times at Eastbridge: 12:00, 12:15, 12:30, 12:45, 13:00, 13:15, 13:30, 13:45.

So a boat can leave Eastbridge at 12:15, turn around and get back to Eastbridge at 13:45.

So a round trip is 90 min, a one-way trip is 45 min.

So I arrived in Westford at 13:00, and the walk has taken me 1 hour.

The next day…

I leave Eastbridge at 12:00 and cycle to Westford at 6 km/h faster than I walked.

I arrive in Westford when the 11:45 from Eastbridge arrives, i.e. at 12:30, so the trip took 30 min.

I walked x km distance in 1 hour (at x km/h). I cycled it in 30 min at x+6 km/h.

So, I can cycle 2x km in 1 hour. So 2x = x+6. So x = 6.

Therefore the boats go 6 km in 45 min = 8 km/h.

Solution: The boats travel at 8 km/h.