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Water Locks

Braingle.com on

Published in Brain Teasers

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?

Solution:

Depending on how you do business and what you value most, there are actually four possible answers! Did you come up with any of these?

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 a careful planning of the traffic on the canal, i.e. making every lock crossing with TWO boats: one up, one down.

Today's brain teaser courtesy of Braingle.com.