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Math Help - Working Alone

  1. #1
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    Working Alone

    James, by himself, can paint 4 rooms in 10 hours. If he hires June to help, they can do the same job together in 6 hours. If he lets June work alone, how long will it take her to paint 4 rooms?
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  2. #2
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    Quote Originally Posted by symmetry View Post
    James, by himself, can paint 4 rooms in 10 hours. If he hires June to help, they can do the same job together in 6 hours. If he lets June work alone, how long will it take her to paint 4 rooms?
    The general formula is,
    \frac{ab}{a+b}
    Where a,b is the amount of time it takes alone and the fraction is the time together they work.

    Thus, the Man can do it in a=10. The Woman can do it in b hours. Together they spend,
    \frac{10b}{10+b}=6
    Multiply by denominator,
    10b=6(10+b)
    10b=60+6b
    10b-6b=60
    4b=60
    b=15 hours.
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  3. #3
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    ok

    I NEVER knew there was such an equation for solving "working alone" problems.

    How about that?

    I learned something new today.

    Thanks a million!
    Last edited by symmetry; January 11th 2007 at 03:52 PM. Reason: Spelling error.
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  4. #4
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    Quote Originally Posted by symmetry View Post
    I NEVER knew that was such an equation for solving "working alone" problems.
    It is my own little formula that becomes useful at times.

    Thanks a million!
    No you do not need to pay me a million.
    You can pay me a 1 dollar today
    1/2 a dollar tomorrow
    1/3 a dollar the next day
    ...

    That would make me happy.
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  5. #5
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    Quote Originally Posted by symmetry View Post
    James, by himself, can paint 4 rooms in 10 hours. If he hires June to help, they can do the same job together in 6 hours. If he lets June work alone, how long will it take her to paint 4 rooms?
    Another way to look at this problem:

    We know that James can paint 4 rooms in 10 hours; thus, in 30 hours he can paint 12 rooms.

    We know that together they can paint 4 rooms in 6 hours. Thus, in 30 hours, they can point 20 rooms.

    From this, we can see that June can paint 8 rooms in 30 hours. Thus, in order to paint just 4 rooms, it would take 15 hours.
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  6. #6
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    Quote Originally Posted by symmetry View Post
    James, by himself, can paint 4 rooms in 10 hours. If he hires June to help, they can do the same job together in 6 hours. If he lets June work alone, how long will it take her to paint 4 rooms?
    James paints 4/10=0.4 rooms per hour
    suppose June paints x rooms per hour.

    Together they paint x+0.4 rooms per hour.

    They paint 4 rooms in 6 hours so their combined rate is 4/6=2/3 rooms per hour

    So x+0.4=0.66.., so x=2/3-2/5=4/15 rooms per hour.

    Time for June to paint 4 rooms = 4/x =4*15/4=15 hours.

    RonL
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