Results 1 to 2 of 2

Thread: A "work" word problem, need help!

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    1

    A "work" word problem, need help!

    This problem is driving me nuts, help would be greatly appreciated.


    "One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?"


    If they worked at the same time, i know the answer is just under 5 hours total...but the first person has to work 2 hours less, and i dont know how to insert that in.

    Any ideas? thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,854
    Thanks
    137
    Quote Originally Posted by itokai View Post
    This problem is driving me nuts, help would be greatly appreciated.


    "One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?"


    If they worked at the same time, i know the answer is just under 5 hours total...but the first person has to work 2 hours less, and i dont know how to insert that in.

    Any ideas? thanks!
    Let W denote the total amount of work which should be done. Then the first person is doing \frac W8 per hour and the second person is doing \frac W{12} per hour.

    Let t denote the working time (in hours!) of the second person. Then the first person works only (t - 2) hours. Therefore the complete work is done:

    \frac W8 (t-2) + \frac W{12} t = W

    Divide by W, expand the brackets and collect like terms:

    \frac5{24} t = \frac 54~\implies~\boxed{t = 6\ h}

    Since your question asks "...how many hours will it take them working together?" the answer is 4 hours.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Oct 17th 2011, 02:50 PM
  2. Replies: 2
    Last Post: Aug 6th 2011, 03:00 PM
  3. Replies: 2
    Last Post: Jul 22nd 2010, 10:15 AM
  4. Replies: 2
    Last Post: Jul 21st 2010, 05:54 PM
  5. Replies: 2
    Last Post: Dec 26th 2008, 04:57 PM

Search Tags


/mathhelpforum @mathhelpforum