Question 1177971: If 3 cats catch 6 rats in 9 days, 9 cats can catch 12 rats in how many days?
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52803)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The other tutor presented a perfectly good formal method for solving the problem; you should understand that method and be able to use it.
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....
3 cats, 6 rats, 9 days (given)
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
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
ANSWER: 6 days for 9 cats to catch 12 rats.
Without all the words of explanation, you can see the process is rather easy:
3 cats, 6 rats, 9 days (given)
9 cats, 18 rats, 9 days
9 cats, 12 rats, 6 days
You will always have different paths you can follow to get the answer using this method. Here is another path:
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)
Answer by josgarithmetic(39620)  (Show Source):
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