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Math Help - Officer K and M

  1. #1
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    Officer K and M

    While working the evening shift, Officer K took 8 hours to complete a task at his work station and Officer M took 10 hours to complete the same task at his work station. How many hours would it take Officer K and Officer M to complete the same task working together, each working at his own work station?

    The answer was 3 but i have no idea how to solve this problem
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  2. #2
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    Re: Officer K and M

    Convert each piece of information from "hours per task" to "tasks per hour" and give it some more thought.
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  3. #3
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    Re: Officer K and M

    Oooooo so i did that but i dont get how you get from off. K 1/4 and off. M 1/5 to 3 hours
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  4. #4
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    Re: Officer K and M

    Quote Originally Posted by japomeanssmile View Post
    While working the evening shift, Officer K took 8 hours to complete a task at his work station and Officer M took 10 hours to complete the same task at his work station. How many hours would it take Officer K and Officer M to complete the same task working together, each working at his own work station?

    The answer was 3 but i have no idea how to solve this problem
    1. Let P denote the result of the task (Remark: I have to choose a letter different from t).

    Then the "working-speed" of K is s_w(K)=\frac P8 and

    the "working-speed" of M is s_w(M)=\frac P{10}

    2. Both officers work t hours together to complete the task:

    \frac P8 \cdot t + \frac P{10} \cdot t = P

    • Factor out P \cdot t
    • Divide through by P
    • Divide by the value of the bracket


    3. I didn't get the given result. Maybe there is a typo in your book?
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  5. #5
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    Re: Officer K and M

    JOB(1/8 + 1/10) = 1 hour
    JOB = ? hours

    Answer is NOT 3 (as earboth says)
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  6. #6
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    Re: Officer K and M

    When two or more people work together (or several machines, or pumps filling a pool, etc.) the rates of work add. Here, one officer does the job in 10 hours so his rate is (1/10) "job per hour". The other officer does the job in 8 hours so his rate is (1/8) "job per hour". Together they will work at 1/10+ 1/8= 2/20+ 5/20= 7/20 "job per hour".

    Once again, the answer is NOT "3 hours" but it is close to that. Perhaps your textbook round off to the nearest hour. Perhaps it took "how many hours" seriously!
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  7. #7
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    Re: Officer K and M

    Quote Originally Posted by HallsofIvy View Post
    Together they will work at 1/10+ 1/8= 2/20+ 5/20= 7/20 "job per hour".
    You need another coffee, Halls!
    1/10 + 1/8 = 4/40 + 5/40 = 9/40 ; makes combined time = 4 4/9 hours.
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