If 3 cats eat 3 mice in 3 minutes; how many cats for 100 mice in 100 minutes?

[ikos9lives]

It would depend on if the 3 cats each 3 mice total in 3 minutes, or eat 3 mice each in 3 minutes.

1 mice per minute: 100 mice in 100 minutes.-3 cats

3 mice per minute: 100 mice in 33.3 minutes-1 cat.

 

[The legend]

who cares about how many... just open a pet shop!

 

[M Grandin]

3 cats 3 mice 3 min --- ? cats 100 mice 100 min

The task may also be solved in two independent steps:

1) To increase 3 mice to 100, the number of cats multiplied by 100/3 :

3 x (100/3) cats 100 mice 3 min

2) To increase 3 min to 100 the number of cats multiplied by 3/100 :

3 x (100/3) x (3/100) = 3 cats 100 mice 100 min

 

[notsosmartman]

im guessing it takes 1 cat to eat 1 mouse in 1 minute... give the same 3 cats 100 minutes they will eat 100 mice ?

 

[I like Serena]

You're all reading the question wrong.
3 cats eat 3 mice in 3 minutes, so each cat eats 1 mouse in 1 minute.
The answer is that 1 cat eats 100 mice in 100 minutes.
This must be the proper answer, because the other interpretation leaves us with a 1/3 mouse that gives ambiguity in the answer and a solution should not be ambiguous.

 

[dextercioby]

They're supposed to eat at the same time. :D

 

[JaredJames]

You're all reading the question wrong.
3 cats eat 3 mice in 3 minutes, so each cat eats 1 mouse in 1 minute.
The answer is that 1 cat eats 100 mice in 100 minutes.
This must be the proper answer, because the other interpretation leaves us with a 1/3 mouse that gives ambiguity in the answer and a solution should not be ambiguous.

No, if three cats take three minutes to eat three mice that means it takes each cat three minutes to eat one mouse.

So it can't be 100 mice in 100 minutes.

 

[I like Serena]

They're supposed to eat at the same time. :D

I thought each cat had 3 mice to eat, making a total of 9 mice.
The wording of the question does not seem to prohibit that.
That is: 3 cats eat 3 mice (each) in 3 minutes.

 

[JaredJames]

I thought each cat had 3 mice to eat, making a total of 9 mice.
The wording of the question does not seem to prohibit that.
That is: 3 cats eat 3 mice (each) in 3 minutes.

No, if it meant each it would have said each. That completely changes the question.

 

[Dale]

So it is 3 cat-minutes per mouse, which means 300 cat-minutes for 100 mice. To accomplish 300 cat-minutes of work in 100 minutes requires 3 cats working in principle. However, this is not taking into account the overhead required for team meetings, paperwork, and management, so you need a manager, an extra worker, and a secretary cat for a total of 6 cats. Of course, while one of these expert cats may eat one mouse in 3 minutes for very little reward eating 2 mice in 6 minutes requires more incentives and 3 mice in 9 minutes even more. What is more is that the incentives become much more expensive as the number of mice in a single shift increases. The company had to hire a financial cat to determine the best allocation of resources, and he determined that after 4 mice the incentives become too expensive, so about 25 cats are needed. Now, in principle 25 cats could accomplish the job in about 12 minutes, leaving each cat 88 minutes to spare. So the original manager cat was promoted to upper management decided to recruit "working managers" from within the pool of worker cats and have the worker cats take on most of the additional paperwork requirements that such a large workforce generates. So the final tally is 28 cats.

 

[JaredJames]

So it is 3 cat-minutes per mouse, which means 300 cat-minutes for 100 mice. To accomplish 300 cat-minutes of work in 100 minutes requires 3 cats working in principle. However, this is not taking into account the overhead required for team meetings, paperwork, and management, so you need a manager, an extra worker, and a secretary cat for a total of 6 cats. Of course, while one of these expert cats may eat one mouse in 3 minutes for very little reward eating 2 mice in 6 minutes requires more incentives and 3 mice in 9 minutes even more. What is more is that the incentives become much more expensive as the number of mice in a single shift increases. The company had to hire a financial cat to determine the best allocation of resources, and he determined that after 4 mice the incentives become too expensive, so about 25 cats are needed. Now, in principle 25 cats could accomplish the job in about 12 minutes, leaving each cat 88 minutes to spare. So the original manager cat was promoted to upper management decided to recruit "working managers" from within the pool of worker cats and have the worker cats take on most of the additional paperwork requirements that such a large workforce generates. So the final tally is 28 cats.

If these are British cats then with an expansion of such magnitude you'd be looking at having at least one health and safety executive on top of that. Wouldn't want to get sued for violating safe working practices now would you.

 

[Dale]

If these are British cats then with an expansion of such magnitude you'd be looking at having at least one HSE executive on top of that. Wouldn't want to get sued for violating safe working practices now would you.

Good point, I figured that cats wouldn't have a union, being cats, but I didn't consider lobbies and regulations.

 

[dextercioby]

So it is 3 cat-minutes per mouse, which means 300 cat-minutes for 100 mice. To accomplish 300 cat-minutes of work in 100 minutes requires 3 cats working in principle. However, this is not taking into account the overhead required for team meetings, paperwork, and management, so you need a manager, an extra worker, and a secretary cat for a total of 6 cats. Of course, while one of these expert cats may eat one mouse in 3 minutes for very little reward eating 2 mice in 6 minutes requires more incentives and 3 mice in 9 minutes even more. What is more is that the incentives become much more expensive as the number of mice in a single shift increases. The company had to hire a financial cat to determine the best allocation of resources, and he determined that after 4 mice the incentives become too expensive, so about 25 cats are needed. Now, in principle 25 cats could accomplish the job in about 12 minutes, leaving each cat 88 minutes to spare. So the original manager cat was promoted to upper management decided to recruit "working managers" from within the pool of worker cats and have the worker cats take on most of the additional paperwork requirements that such a large workforce generates. So the final tally is 28 cats.

I like this, 3 normal cats in the hypothesis vs 28 corporate cats )) I will add it to my FB profile, if you don't mind.

 

[I like Serena]

No, if it meant each it would have said each. That completely changes the question.

How do you know?

If the question had been stated properly, it would read either:
A. 3 cats eat a total of 3 mice in 3 minutes, ...
B. 3 cats eat 3 mice each in 3 minutes, ...

As it is, I believe the semantics allow for either interpretation.

 

[BobG]

So it is 3 cat-minutes per mouse, which means 300 cat-minutes for 100 mice. To accomplish 300 cat-minutes of work in 100 minutes requires 3 cats working in principle. However, this is not taking into account the overhead required for team meetings, paperwork, and management, so you need a manager, an extra worker, and a secretary cat for a total of 6 cats. Of course, while one of these expert cats may eat one mouse in 3 minutes for very little reward eating 2 mice in 6 minutes requires more incentives and 3 mice in 9 minutes even more. What is more is that the incentives become much more expensive as the number of mice in a single shift increases. The company had to hire a financial cat to determine the best allocation of resources, and he determined that after 4 mice the incentives become too expensive, so about 25 cats are needed. Now, in principle 25 cats could accomplish the job in about 12 minutes, leaving each cat 88 minutes to spare. So the original manager cat was promoted to upper management decided to recruit "working managers" from within the pool of worker cats and have the worker cats take on most of the additional paperwork requirements that such a large workforce generates. So the final tally is 28 cats.

How do you know?

If the question had been stated properly, it would read either:
A. 3 cats eat a total of 3 mice in 3 minutes, ...
B. 3 cats eat 3 mice each in 3 minutes, ...

As it is, I believe the semantics allow for either interpretation.

Better add a team of lawyer cats to interpret the wording the contract. Counting the HSE, I think you're up to 35 cats.

 

[Dale]

Fat cat lawyers. We humans seem to have a surplus.

 

[Physics-Learner]

i know this seems simple, and perhaps it's a trick, but I'm confused! is the answer 100?

boy, you guys can sure drag a thread out. however, i don't think there is room for semantics, if you want to be serious.

and there is no need for sharing of mice. the point is that the rate is the same, so it takes the same number of cats.

the answer, of course, is 3.

the "trick" is that most people will say 100, if they don't give it much thought. 3-3-3 and x-100-100.

it is easy to fill in the x with 100.

 

[ashishsinghal]

the answer is easy. it just depends on the time taken to eat one mouse.

 

[Sybren]

Dimensional analysis has helped me here.
It takes 3 cats 3 minutes to eat 3 mice, so the eating rate is (introducing the useful unit catminute=cat * minute):
3 mice/ 3 cats / 3 minutes = 1/3 mouse cat^-1 minute^-1 = 1/3 mouse per catminute.

100 mice / x cats / 100 minutes = 1/x mouse per catminute

If the eating rate is determined at 1/3 mouse per catminute, then clearly

3 cats will eat 100 mice in 100 minutes!
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[Darken-Sol]

1 unless it belongs to schroedinger, then it may or it may not.

 

[Darken-Sol]

i actually was being facetious, the answer didnt hit me till i was turning beer to water. it seem you need 3 cats to keep up the rate of 1 mouse per minute.

 

[AwesomeSN]

Seems to be more of a question of wording than mathematics according to you guys haha