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Thread: Word problem

  1. #1
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    Word problem

    so i missed this lesson and i cant seem to figure out what to do, ill just simplify the word problem....basically.

    person 1 complete job in m-5 minutes
    person 2 completes the job in m minutes
    person 3 completes the job in same amount of time as person 2
    together they take 3.23 minutes to complete the job... how long does person 2 take to finish the job?

    tanks in advance
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  2. #2
    MHF Contributor Unknown008's Avatar
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    You use this formula:

    $\displaystyle \dfrac{1}{t_1} + \dfrac{1}{t_2} + \dfrac{1}{t_3} = \dfrac{1}{t_{total}}$

    Can you give it a try?
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  3. #3
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    i tried about 5 times and i cant seem to get the right answer. im thinking the answer at the back of the book is wrong. can someone give it a try?
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  4. #4
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    word problem

    Hi baffz,
    Substitute the values in the given equation t1 = 5 , t2 =m, t3 = m and the sum =1/3.23 and yes 2 and 3 are slow workers


    bjh
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  5. #5
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    wouldnt i sub in m-5 into t1?
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  6. #6
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    Hello, Baffz!

    $\displaystyle \text{Person }A\text{ completes the job in }m-5\text{ minutes.}$
    $\displaystyle \text{Person }B\text{ completes the job in }m\text{ minutes.}$
    $\displaystyle \text{Person }C\text{ completes the job in }m\text{ minutes.}$
    $\displaystyle \text{Together they complete the job in 3.23 minutes.}$

    $\displaystyle \text{How long does person }B\text{ take to complete the job alone?}$

    Here is the reasoning behind that mysterious equation . . .

    Person $\displaystyle \,A$ does the job in $\displaystyle m-5$ minues.
    . . In one minute, he can do $\displaystyle \frac{1}{m-5}$ of the job.
    (Note that $\displaystyle \,m \,>\,5$)

    Person $\displaystyle \,B$ does the job in $\displaystyle \,m$ minutes.
    . . In one minute, he can do $\displaystyle \frac{1}{m}$ of the job.

    Person $\displaystyle C$ does the job in $\displaystyle \,m$ minutes.
    . . In one minute, he can do $\displaystyle \frac{1}{m}$ of the job.

    Working together for one minute, they can do: .$\displaystyle \frac{1}{m-5} + \frac{1}{m} + \frac{1}{m}$ of the job. .[1]


    We are told that, working together, they do the job is 3.23 minutes.
    . . In one minute, they can do $\displaystyle \frac{1}{3.23}$ of the job. .[2]


    We just described the amount of work done in one minute in two ways.


    Equate [1] and [2]: .$\displaystyle \displaystyle \frac{1}{m-5} + \frac{1}{m} + \frac{1}{m} \;=\;\frac{1}{3.23}$

    . . There is our equation!


    Multiply by $\displaystyle 3.23m(m-5)\!:$

    . . $\displaystyle 3.23m + 3.23(m-5) + 3.23(m-5) \:=\:m(m-5)$


    This simplifies to: .$\displaystyle m^2 - 14.69m + 32.3 \:=\:0$


    Quadratic Formula:

    . .$\displaystyle \displaystyle m \;=\;\frac{14.69 \pm \sqrt{14.69^2 - 4(1)(32.3)}}{2(1)} \;=\;\frac{14.69 \pm \sqrt{86.5961}}{2} $

    . . . . . $\displaystyle =\;\dfrac{14.69 \pm 9.305702553}{2} \;=\;\begin{Bmatrix} 2.692148724 \\ 11.99785128 \end{Bmatrix}$


    Take the larger value: .$\displaystyle m \:\approx\:12$


    Working alone, person $\displaystyle \,B$ would take 12 minutes to do the job.

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  7. #7
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    Sorry baffz I misread the time for person 1 .It would have been clearer if the times for each were expressed in t and t-5

    bjh
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  8. #8
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    thanks soroban thats the correct answer but im not understanding why i multiply by 3.23m(m-5)?

    EDIT: is it because those are the denominators?
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  9. #9
    MHF Contributor Unknown008's Avatar
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    Yes, to remove all the fractions.
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