SOLUTION: if 7 girls take 1 hour to do work how many hours will 3 girls take?

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Question 1193949: if 7 girls take 1 hour to do work how many hours will 3 girls take?
Found 4 solutions by josgarithmetic, mccravyedwin, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!


1, for the right-side member of both for both situations representing the "work", same value in each situation;

-------for just three girls to do this work.
Answer by mccravyedwin(406)   (Show Source): You can put this solution on YOUR website!
Here's a different approach. Think of the least common multiple 
of 7 and 3, which is 21.

if 7 girls take 1 hour to do work how many hours will 3 girls take?
3 times as many girls could do the work 3 times as fast or in only 1/3 of an hour.

That is, 21 girls could do the work in 20 minutes.

So 1/7 as many girls as that would take 7 times as long.

That is, 3 girls would take 20*7=140 minutes, which is 1 hour and 20 minutes.

Edwin
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

The standard mantra to pronounce solving this one and thousand other similar problems sounds this way 

    The entire job is 7 girl-hours.

    Three girls can do it in   hours = 2  hours.    ANSWER

Solved.

It is worth to  MEMORIZE  it.

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

Reacting on the @greenestamps attacks on me,  the more words you will pronounce
solving such simple problems,  the more and more the solution and its meaning will elude from you.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


Don't pay a lot of attention to tutor @ikleyn's "standard mantra" for how to solve this kind of problem. There are numerous ways to solve them; what is her favorite ("standard") way of solving them isn't going the be everybody's favorite method.

I would simply use common sense to solve this problem. If the "new" number of girls is 3/7 of the original number, then the amount of time required to do the work is 7/3 as much.

ANSWER: (7/3) of 1 hour, or 7/3 hours, or 2 1/3 hours, or 2 hours 20 minutes.

If you want to be just a bit more formal with this same solution path, you can say that the number of hours required to do the work is inversely proportional to the number of workers (more workers means less time; fewer workers means more time), so 3/7 as many workers means (1/(3/7)) = 7/3 times as many hours.

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In response to the note from tutor @ikleyn about my "attacking" her....

Yes, tutor @ikleyn, I will ABSOLUTELY attack you any time you tell a student that your way of solving a problem is THE way.

This kind of problem is very easily solved using common sense. If you don't have common sense and want to solve the problem using the concept of "girl-hours", then that's fine. But don't tell students that is the only way to solve the problem.

And don't "attack" me for suggesting that the student solve the problem using logical reasoning instead of formal mathematics.
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