Question 1177971
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The other tutor presented a perfectly good formal method for solving the problem; you should understand that method and be able to use it.<br>
For a relatively simple problem like this, I prefer a more informal solution method, changing two of the parameters at a time using common sense, like this....<br>
3 cats, 6 rats, 9 days (given)<br>
The specified number of cats is 9.  More cats in the same number of days means more rats.  So multiply the number of cats by 3 to get the required 9 cats, and multiply the number of rats by 3:
3 cats, 6 rats, 9 days (given)
9 cats, 18 rats, 9 days<br>
The specified number of rats is 12. Fewer rats with the same number of cats means fewer days.  So multiply the 18 rats by 2/3 to get the required 12 rats, and multiply the number of days by 2/3:
3 cats, 6 rats, 9 days (given)
9 cats, 18 rats, 9 days
9 cats, 12 rats, 6 days<br>
ANSWER: 6 days for 9 cats to catch 12 rats.<br>
Without all the words of explanation, you can see the process is rather easy:<br>
3 cats, 6 rats, 9 days (given)
9 cats, 18 rats, 9 days
9 cats, 12 rats, 6 days<br>
You will always have different paths you can follow to get the answer using this method. Here is another path:<br>
3 cats, 6 rats, 9 days (given)
3 cats, 12 rats, 18 days (same number of cats, twice as many rats means twice as many days)
9 cats, 12 rats, 6 days (3 times as many cats, same number of rats means one-third as many days)<br>