Work...1

Discussion in 'Algebra' started by nycmathguy, Feb 23, 2022.

  1. nycmathguy

    nycmathguy

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    Is my set up right?

    1. Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?

    Jane = 1/5

    Paul = 1/6

    Peter = 1/t

    Let t = length of time it will take Peter to finish the job alone.

    Total time = 2 hours

    1/5 + 1/6 + 1//t = 2

    Yes?

    2. Jim can dig a hole by himself in 12 hours. John can do it in 8 hours. Jack can do it in 6. How long will it take them if they all work together?

    Jim = 1/12

    John = 1/8

    Jack = 1/6

    Let t = length of time for all three to finish the job.

    1/12 + 1/8 + 1/6 = 1/x

    Yes?
     
    nycmathguy, Feb 23, 2022
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  2. nycmathguy

    Country Boy

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    Perhaps a little picky, but "Jane" is a person, not a number! I would never say "Jane= 1/5".
    It would be better to say, "Since Jane paints the fence in 5 hours working alone, she paints at a rate of 1/5 fence per hour".

    Yes, when people work together their rates of work add.
     
    Country Boy, Feb 23, 2022
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  3. nycmathguy

    nycmathguy

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    If Jane paints for 5 hours, then she painted for 5 hours. I don't understand the rate part of the question for each person.
     
    nycmathguy, Feb 23, 2022
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  4. nycmathguy

    MathLover1

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    1.
    Jane does the job alone she can finish it in 5 hours: rate 1/5
    if Paul does the job alone he can finish it in 6 hours: rate 1/6
    Peter: let x represent the time it would take Peter solo, so his rate is 1/x
    all together can finish painting the fence in 2 hours: rate 1/2

    the sum of individual rates must be equal to rate when all work together

    1/5 + 1/6 + 1/x = 1/2

    Solving for x

    6x + 5x + 30 = 15x |Multiplying thru by 30x so as all denominators = 1
    30 = 4x
    x = 30/4 or 7.5 hrs,

    time it would take Peter solo is 7.5 hrs

    note: The formula for “Work” Problems that involve three persons is:

    [​IMG]


    2.
    Let t = length of time for all three to finish the job.
    Jim = (1/12)t
    John = (1/8)t
    Jack = (1/6)t

    adding all will be equal to 1 (1 job done)

    (1/12) t+ (1/8)t + (1/6 )t= 1
    (3t)/8= 1
    3t= 8
    t= 8/3
    t=2hours and 40 min
     
    MathLover1, Feb 23, 2022
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    nycmathguy likes this.
  5. nycmathguy

    Country Boy

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    If it takes a person 5 hours to do one job, how much of the job does the person do each hour?

    Doing one job in 5 hours is (1 job)/(5 hours)= (1/5) (job/hour) or 1/5 "job per hour'=
     
    Country Boy, Feb 23, 2022
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  6. nycmathguy

    nycmathguy

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    Thank you. Country Boy is now on my ignore list. I can't learn math with someone like him on the team.
     
    nycmathguy, Feb 23, 2022
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