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Puzzling Adventures Main Puzzle Solution - September 2008




Cloe Liane Shasha

Solutions:

1. The lowest-energy way to go is to use:
a) The slowest speed on the lake (water speed = 5 kmh; energy = 6 kWh);
b) The slowest speed on the 18-km portion with a 2-kmh downstream current (water speed = 5 kmh, land speed = 3 kmh and energy = 6 kWh);
c) The fastest speed on the 24 km portion (water speed = 15 kmh, land speed = 8 kmh and energy = 15 kWh).

That plan would take 6 + 6 + 3 = 21 hours and would consume a total of 27 kWh.

2. One thing you could do is to go faster on the lake. If you go 10 kmh, you would save 3 hours and consume 3 more kWh. That is not the best thing you could do, however. You would do better if you increased your water speed to 15 kmh on the 18-km portion: doing so would increase your energy consumption by less than 0.93 kWh but decrease your time by 4.62 hours. That strategy would leave you a bit more than 2.0 kWh. You can use that energy only on the 30-km lake journey. Suppose that you go from a water speed of 5 kmh to 10 kmh after 4 hours. So, in the first 4 hours you travel 20 km. Then you travel the last 10 km in 1 hour. This would consume the 2 kWh you have left but save an additional hour. So, you can make the trip in about 21 - 5.6 = 15.4 hours on 30 kWh of energy.

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