Mark
CATS/RATS
12
CATS & RATS II
Assuming that the cats are occupied by a rat until it is dead (can't leave partially dead rats for other cats to finish off):
C. 14 - Twelve cats can kill 96 in 48 minutes. Another pair of cats is required to kill the other four.
D. 13 - Twelve cats can kill 96 rats in 48 minutes.
Another cat is required to kill the other four.
I have been asked if I give Mark the answers.
Let me make it quite clear, I often don't even give the question.
This is a good example of a phenomenon that often occurs in working problems in double proportion; the answer looks all right at first, but, when we come to test it, we find that, owing to peculiar circumstances in the case, the solution is either impossible or else indefinite, and needing further data. The 'peculiar circumstance' here is that fractional cats or rats are excluded from consideration, and in consequence of this the solution is, as we shall see, indefinite.
The solution, by the ordinary rules of Double Proportion, is as follows:
Code:
6 rats : 100 rats \
> :: 6 cats : ans.
50 min. : 6 min. /
.
. . ans. = (100)(6)(6)/(50)(6) = 12
But when we come to trace the history of this sanguinary scene through all its horrid details, we find that at the end of 48 minutes 96 rats are dead, and that there remain 4 live rats and 2 minutes to kill them in: the question is, can this be done?
In cases A and B it is clear that the 12 cats (who are assumed to come quite fresh from their 48 minutes of slaughter) can finish the affair in the required time; but, in case C, it can only be done by supposing that 2 cats could kill two-thirds of a rat in 2 minutes; and in case D, by supposing that a cat could kill one-third of a rat in two minutes. Neither supposition is warranted by the data; nor could the fractional rats (even if endowed with equal vitality) be fairly assigned to the different cats. For my part, if I were a cat in case D, and did not find my claws in good working order, I should certainly prefer to have my one-third-rat cut off from the tail end.
In cases C and D, then, it is clear that we must provide extra cat-power. In case C *less* than 2 extra cats would be of no use. If 2 were supplied, and if they began killing their 4 rats at the beginning of the time, they would finish them in 12 minutes, and have 36 minutes to spare, during which they might weep, like Alexander, because there were not 12 more rats to kill. In case D, one extra cat would suffice; it would kill its 4 rats in 24 minutes, and have 24 minutes to spare, during which it could have killed another 4. But in neither case could any use be made of the last 2 minutes, except to half-kill rats---a barbarity we need not take into consideration.
To sum up our results. If the 6 cats kill the 6 rats by method A or B, the answer is 12; if by method C, 14; if by method D, 13.
A body of soldiers form a 50m-by-50m square ABCD on the parade ground. In a unit of time, they march forward 50m in formation to take up the position DCEF.
The army's mascot, a small dingo, is standing next to its handler at location A. When the soldiers start marching, the dog begins to run around the moving body in a clockwise direction, keeping as close to it as possible. When one unit of time has elapsed, the dingo has made one complete circuit and has got back to its handler, who is now at location D.
(We can assume the dingo runs at a constant speed and does not delay when turning the corners.)
Code:
B----C----E
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A----D----F
How far does the dingo travel
