SOLUTION: If 3 cats catch 6 rats in 9 days, 9 cats can catch 12 rats in how many days?

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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(52810)   (Show Source): You can put this solution on YOUR website!
.

Let  d  be "in how many days . . . ".


Then you have this proportion


     = ,    (1)

or

     = .     (1)

     = .


The proportion says that the rate   is the same in both cases.


From proportion  (1),  you have


    9d =  = 2*27

     d =  = 2*3 = 6 days.      AMSWER

Solved.

By doing this way,  you will  ALWAYS  feel the solid ground under your legs and will  NEVER  make an error.

----------------

To see many other similar  (and different)  problems,  solved in this way,  look into the lesson
    - Rate of work problems
in this site.



Answer by greenestamps(13203)   (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): You can put this solution on YOUR website!

N, how many doing the catching
R, rate for 1 cat
T, time
J, the amount of catches







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