Chip made ecxellent point about the key issue. The key to the problem is the reference point. In reference to the water sailing boat will win but in reference to the ground it will be opposite. And the ground is the key reference as the racing comitee boat is anchored firmly to the ground and finish line is stationary to the gound - not water.
To reiterate:
Each case is totally independednt to each other.
In reference to the water the boat without additional wind will move faster then the other and can cover more distance over water toward finish.
In reference to the ground it will fall behind in progres over the ground despite the current!!!!
The ground is the key reference for judging progreess toward finish.
Correct solution to the problemm looks like total paradox but is is not and it is explainable by physics and balance of energy. It is totally opposite to what "common sense" will suggest.
sailing puzzle
Surprisingly this thread is still active.
As Kaz mention - reference point is very important, but he made wrong conclusions.
I wrote before that it would be convenient to mark water as a reference with floating buoy for both boats. This buoy will not be affected by wind and will float with water, thus they will go the distance in the same time for both cases.
Now consider the boats progress relative to that buoy.
The first sailor (5 kt current and no wind) will have 5 kt apparent head wind. If you look relative to the water buoy - the picture is that wind blow you back (as if there no current), but you can tuck and thus can make progress ahead of the bouy.
The second sailor (with 5 kt current and 5 kt wind) relative to the water bouy will be in a complete calm - he can not do anything. Does not matter if he has his sails up or down he will float just with the current speed.
Since the first sailor can (at least somehow) make progress ahead of the bouy, this means that he has a chance to win (he also has a chance to loose if he apears to be a sloppy sailor. There is nothing the second guy can do to win or loose, by the way.
As Kaz mention - reference point is very important, but he made wrong conclusions.
I wrote before that it would be convenient to mark water as a reference with floating buoy for both boats. This buoy will not be affected by wind and will float with water, thus they will go the distance in the same time for both cases.
Now consider the boats progress relative to that buoy.
The first sailor (5 kt current and no wind) will have 5 kt apparent head wind. If you look relative to the water buoy - the picture is that wind blow you back (as if there no current), but you can tuck and thus can make progress ahead of the bouy.
The second sailor (with 5 kt current and 5 kt wind) relative to the water bouy will be in a complete calm - he can not do anything. Does not matter if he has his sails up or down he will float just with the current speed.
Since the first sailor can (at least somehow) make progress ahead of the bouy, this means that he has a chance to win (he also has a chance to loose if he apears to be a sloppy sailor. There is nothing the second guy can do to win or loose, by the way.
I do agree that my conclusion seems to be wrong . But I analysed several many different combination of wind and current and in all other cases the boat with extra wind (extra energy source) had advantage. The conditions decribed by puzzle look like exception from many other possible situations. Because the macro world is continuous and physics prinicples must always apply, I had no other choice but to conclude that obvious answer must be wrong otherwise it will violate universal rules of physics. Having to choose answer that look right and is in disagreement with physics and the one which looks wrong but agrees with universal laws of newtonian physics - there is no choice - but to follow Newton - even if it seems to be wrong and I may not like it.