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Thread: Working Alone

  1. #1
    Member harpazo's Avatar
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    Working Alone

    Patrice, by himself, can paint 4 rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint the room?

    Let x = length of time it will take April to paint the room alone.

    Patrice = 1/10

    April = 1/x

    Together = 1/6

    (1/10) + (1/x) = (1/6)

    Correct?
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  2. #2
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    Re: Working Alone

    Yes, that is the correct equation but it would better to say what
    "Patrice = 1/10
    April = 1/x
    Together = 1/6"

    MEAN!
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  3. #3
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    Re: Working Alone

    Quote Originally Posted by harpazo View Post
    Patrice, by himself, can paint 4 rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint the room?
    Let x = length of time it will take April to paint the room alone.
    Patrice = 1/10
    April = 1/x
    Together = 1/6
    (1/10) + (1/x) = (1/6)
    Correct?
    What happened to the four rooms? Where are they in the setup?
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  4. #4
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    Re: Working Alone

    Apparently "the job" consists of painting 4 rooms. Since the problem asks about "the job" the individual rooms are irrelevant.

    But, yes, the wording should be "If he lets April work alone, how long will it take her to do the job and
    "Let x= the length of time it would April to do the job alone"

    and to say:
    The rate at which Patrice works= 1/10
    The rate at which April works= 1/x
    The rate at which they work together= 1/6.

    (I hate wording like "Patrice= 1/10" and "April= 1/x". Patrice and April are people, not numbers!)
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  5. #5
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    Re: Working Alone

    Quote Originally Posted by harpazo View Post
    Patrice, by himself, can paint 4 rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours.
    If he lets April work alone, how long will it take her to paint the room?
    Quote Originally Posted by HallsofIvy View Post
    Apparently "the job" consists of painting 4 rooms. Since the problem asks about "the job" the individual rooms are irrelevant.
    Actually it does say "If he lets April work alone, how long will it take her to paint the room one room.
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    Re: Working Alone

    Quote Originally Posted by harpazo View Post
    Patrice, by himself, can paint 4 rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours.
    If he lets April work alone, how long will it take her to paint the rooms?

    Let x = length of time it will take April to paint the rooms alone.
    .
    .
    .
    harpazo, the first time around the word "rooms" was used. So, it makes sense that "rooms" would continue to be used, not "room" and especially
    not "the room," because there is no distinct/particular room.
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  7. #7
    Member harpazo's Avatar
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    Re: Working Alone

    Quote Originally Posted by HallsofIvy View Post
    Yes, that is the correct equation but it would better to say what
    "Patrice = 1/10
    April = 1/x
    Together = 1/6"

    MEAN!
    Quote Originally Posted by Plato View Post
    What happened to the four rooms? Where are they in the setup?
    I don't know what this means. I am just following the examples for this particular question.
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  8. #8
    Member harpazo's Avatar
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    Re: Working Alone

    (1/10) + (1/x) = (1/6)

    3x + 30 = 5x

    3x - 5x = -30

    -2x = -30

    x = -30/-2

    x = 15

    Alone, April can paint four rooms in 15 hours.
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