Water Locks
Logic puzzles require you to think. You will have to be logical in your reasoning.
A canal in UK has 13 locks and no water supply at the top.
Each lock loses 7000 L of water when used.
A truck capable of carrying 22 tons of water is rented to bring water from the bottom to the top.
Is the contract reasonable, and why?
HintWhere are the water losses?
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Answer
At first thought:
We could think that 13 x 7,000 litres = 91,000 litres that would be lost, against 22 tons.
22 tons equal 22,000 Litres (1 ton of water = 1000 kg = 1000 litres = 1 m3).
So we would lose 91,000 litres to gain 22,000 litres: contract is not worth it.
On second thought:
Certainly, each lock loses 7,000 litres, but it takes the water from the level above!
Hence, by succession, we only lose 7,000 litres from the top level, no matter how many locks we have!
The balance, then, is 22,000 litres - 7,000 litres = 15,000 litres: the contract is worth it!
On third thought (the engineering approach):
Unfortunately, waterways "lose" water in a continuous manner: by evaporation, by "leaks" to the underground water table, by "leaks" through the locks.
Now come two more factors: the length of the canal (which determines the evaporation and leaks to underground), and the TIME it takes to bring the water upstream.
If the whole of the canal loses 3,000 litres/hour and it takes the boat 5 hours to reach the top, the exercise is pointless (just maintaining the levels). Less time, and it is worth it. More time, and it is worthless.
On fourth thought (the economics):
If the engineering balance is "close to equilibrium", economics may make the exercise worthwhile, by careful planning of the traffic on the canal, i.e. making every lock crossing with TWO boats: one up, one down.
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Comments
cathalmccabe
Mar 13, 2002
| I like the consideration of all the possibilities! |
mad-ade  
Mar 23, 2002
| THIS ISN'T A PUZZLE, ITS AN ESSAY. LOL |
rayneeday
Mar 27, 2002
| Only the Brits would build a bunch of lochs with no water supply, Must have been a government operation!!!!! |
Canary05
Aug 29, 2002
| I thought that it was the metric one TONNE of water equals 1000 litres, not the imperial one ton. |
Gizzer
Sep 23, 2002
| If there is no water supply at the top, then on what will the boat sail when it gets to the top? |
(user deleted)
Apr 13, 2006
| Em.. considering archimedes' principle once the ship enters the canal its gonna displace an enormous quantity of water which will be approximately as much water as it contains so it is completely unfeasible, theres no point in considering any other scenario. |
eyenowhour
Jan 09, 2007
| There were just too many thoughts in this puzzle for me... |
calmsavior
Mar 27, 2007
| where's the answer... |
(user deleted)
Jul 13, 2007
| Here is another possibility.
The contract is taken out on a TRUCK to carry water to the top of the canal. 22 Tons of water is quite a bit however there is nothing saying that the truck does not have wheels and as such, takes the road to the top of the canal and thus loses no water. |
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