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Thread: Ratio Proportion: it takes 30 minutes for 3 people to clean four identical rooms.

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  1. #1
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    Ratio Proportion: it takes 30 minutes for 3 people to clean four identical rooms.

    could somebody help me with this question:-

    it takes 30 minutes for 3 people to clean four identical rooms. How long would it take 9 people to clean 12 of the same rooms at the same rate

    I find he Phrase "Same rate" confusing. My answer is 30 minutes but my teacher says it is 90 minutes and I can't understand why

    This is how I did it:-
    3 People = 4 rooms in 30 minutes
    Divide LHS by 3 and multiply RHS with 3

    1 People = 4 rooms in 90 minutes
    multiply LHS by 9 and Divide RHS with 9

    9 People = 4 rooms in 10 minutes
    Multiply RHS with 3
    9 People = 12 rooms in 30 minutes
    Answer 30 Minutes

  2. #2
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    Quote Originally Posted by MAMM View Post
    could somebody help me with this question:-

    it takes 30 minutes for 3 people to clean four identical rooms. How long would it take 9 people to clean 12 of the same rooms at the same rate

    I find he Phrase "Same rate" confusing. My answer is 30 minutes but my teacher says it is 90 minutes and I can't understand why

    This is how I did it:-
    3 People = 4 rooms in 30 minutes
    Divide LHS by 3 and multiply RHS with 3

    1 People = 4 rooms in 90 minutes
    multiply LHS by 9 and Divide RHS with 9

    9 People = 4 rooms in 10 minutes
    Multiply RHS with 3
    9 People = 12 rooms in 30 minutes
    Answer 30 Minutes
    As far as I can see, your answer and the process are both correct.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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    Verbal Logic: Triple the Resources and Triple the Task. The time should be the same unless they are tripping over each other.

    Mathematical Logic: [tex]\dfrac{a\cdot c}{b\cdot c}= \dfrac{a}{b}\cdot\dfrac{c}{c} = \dfrac{a}{b}\cdot 1 = \dfrac{a}{b}[/tex]

    Arithmetic (Actually showing the "Rate"):

    3 person * 30 min = 4 room ==> Rate = (4 room)/(90 person * min)

    9 person * X min = 12 room ==> Rate= (12 room)/((9*X) person * min)

    If (4 room)/(90 person * min) = (12 room)/((9*X) person * min) ==> X = ??

    Historical Comment: It's an old joke, actually. If it take 3 cats 3 minutes to eat 3 mice, how long does it take 6 cats to eat 6 mice? It's sill 3 minutes.

    Unless we have the question wrong, your teacher will have to review the material.

  4. #4
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    Cool

    Quote Originally Posted by MAMM View Post
    It takes 30 minutes for 3 people to clean four identical rooms. How long would it take 9 people to clean 12 of the same rooms at the same rate?

    I find the phrase "same rate" confusing.
    I would take the phrase as meaning that the people are being regarded as interchangeable (rather than some of them being faster or slower than some others), and that they complete the same amount of work in the same amount of time, regardless of how many people are there (so nobody gets in anybody else's way).

    Quote Originally Posted by MAMM View Post
    My answer is 30 minutes but my teacher says it is 90 minutes and I can't understand why
    Here's another way of doing this:

    If three people can clean four rooms in half an hour, then they can clean eight rooms in an hour. (A full hour can be easier to work with.)

    "Three people working for one hour" is three man-hours. So eight rooms require three man-hours. Dividing, we find that one room requires 3/8 of a man-hour.

    They now want us to consider twelve rooms. Multiplying, we find that this will require 9/2 man-hours. If we split this between nine workers, then we find that they take 1/2 of an hour.

    So your answer is correct. Maybe the teacher should be required to show his/her work...?

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