SOLUTION: If 5 cats catch 5 rats in 5 minutes, how many cats are needed to catch 72 rats in 2 hours? Thanks!!

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Question 1200124: If 5 cats catch 5 rats in 5 minutes, how many cats are needed to catch 72 rats in 2 hours?

Thanks!!
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You can write a basic work rates rule from the IF clause, or just go straight to one cats work rate is 1%2F5, in RAT/MINUTES.


How many cats, n, catch 72 rats in 2 hours?
2 hours is 120 minutes.
n%281%2F5%29%2A120=72
n=72%285%2F120%29
highlight%28n=3%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The method I personally find easiest to use on a problem like this is to consider how changing the number of rats and the amount of time changes the number of cats required.

More rats means more cats are required, so 72 rats instead of 5 rats means multiply the number of cats required by 72/5.

More time means fewer cats are needed, so 2 hours (120 minutes) instead of 5 minutes means multiply the number of cats required by 5/120.

%285%29%2872%2F5%29%285%2F120%29=%2872%29%281%2F24%29=3

ANSWER: 3 cats

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
If 5 cats catch 5 rats in 5 minutes, how many cats are needed to catch 72 rats in 2 hours?
~~~~~~~~~~~~~~~~~~~~ 

If 5 cats catch 5 rats in 5 minutes, then the rate of each single cat is  

    5_rats%2F%285_cats%2A_5_minutes%29 = 5%2F%285%2A5%29 = 1%2F5.


If "c" cats catch 72 rats in 2 hours, then the rate of each single cat is

    72_rats%2F%28c_cats%2A120_minutes%29 = 6%2F%28c%2A10%29 = 3%2F%28c%2A5%29.


The rates assume to be the same, so you write this proportion (equation)

    3%2F%285c%29 = 1%2F5.


It gives you c = %28%283%2F5%29%29%2F%28%281%2F5%29%29 = 3.


ANSWER.  3 cats.

Solved.

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You can find many other similar solved problems in these lessons
    - Rate of work problems
    - Entertainment problems on joint work
in this site.

My point is that if a person learns on how to solve joint work problems
and does not use a conception of the rate of work,  then this person spends his time for nothing.