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.

5 Comments

1. 1. BenGraham 08:27 PM 9/3/08

   6 + 6 + 3 = 15, last I checked. Not 21.

   Reply | Report Abuse | Link to this

2. 2. BenGraham 08:41 PM 9/3/08

   Also, I find the following to be the most efficient use of the 30 kw battery:
   15 km/h on the 24 km stretch: 3 hours, 15 kw
   15 km/h on the 18 km stretch: 1.38 hours, 6.92 kw
   10 km/h on the first 20 km of the lake: 2 hours, 6 kw
   5 km/h on the remaining 10 km of the lake: 2 hours, 2 kw
   Total consumption: 8.38 hours, 29.92 kw
   

   Reply | Report Abuse | Link to this

3. 3. andres100 11:59 AM 9/4/08

   6+6+3=21 ??????????????

   Reply | Report Abuse | Link to this

4. 4. njroux in reply to 01:05 PM 9/11/08

   My 11 year old says 6+6+3 = 15 not 21 as you say - please fix the answer to your River Run puzzle.

   Reply | Report Abuse | Link to this

5. 5. njroux 01:05 PM 9/11/08

   My 11 year old says 6+6+3 = 15 not 21 as you say - please fix the answer to your River Run puzzle.

   Reply | Report Abuse | Link to this