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math problem..driving me crazy!!!

Discussion in 'DAT Discussions' started by smile101, May 15, 2008.

  1. smile101

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    A construction firm receives an important contract and hires 15 temporary workers in addition to its full-time staff. If the entire full-time staff of 25 could complete the job in five months, and if temporary workers work 5/6 as fast as full-time workers, how much time will be saved by hiring the additional workers?
    A. 1 2/3 mon
    B. 1 7/8 mon
    C. 2 1/6 mon
    D. 2 1/5 mon
    E. 3 1/3 mon

    Please help ya'll!!!
     
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  3. Oh boy I am not sure at all about what I'm about to say but I'm going to try it anyways, and people can comment. So 25 workers can do a job in 5 months, so 1 worker does 1/5 of the job. Now use that rate (1/5) to fine out the total. (25)(1/5) + (15)(1/5)(5/6) = 7.5. I'm flyin by the seat of my pants so I'm not sure what that is. so rate x time = job? so 7.5x=5, x=3.33. so 5-3.33 is 1.66 which is A. Again like I said I have no idea what I did or what my intermediate numbers stand for.
     
  4. Streetwolf

    Streetwolf Ultra Senior Member
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    The full time staff of 25 finishes a job in 5 months. Each temp worker is 5/6 as efficient as the full time worker, and 15 of them are hired. If each temp worker is 5/6 as efficient, then this means you have the equivalent of 15(5/6) = 12.5 full time workers. So in reality you have 37.5 full time workers which is 1.5x (3/2) the original amount. That means the job can be finished in 2/3 the time which would be (2/3)5 = 3 and 1/3 months. So you save 1 and 2/3 months which is choice (A).
     
  5. smile101

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    thanks guys!!!
     
  6. Much better way than mine. Plus, you seemed to know the process while doing it, better than just a hunch.
     
  7. dentalplan

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    Streetwolf: I like your reasoning, but can you explain something to me?

    What exactly is the logical connection between "So in reality you have 37.5 full time workers which is 1.5x (3/2) the original amount."

    and......

    "That means the job can be finished in 2/3 the time"


    For some reason I can't grasp my head around this one....Can you explain, or show logically, exactly how you can assume that 1.5 that amount of full time workers means the job can be done in 2/3 the time?

    I hope you can explain it with more depth than just 3/2 is the reciprocal of 2/3, which is the fraction of time the job will be done.

    I want to know the exact logic behind that ^^

    I just can't make the connection.

    I tried making myself equations...but they just ended up looking like: 25/time= rate. So 25/5 months = rate of 5 men per month. And then dividing 37.5 by that rate (5) to get the new time. Yeah.....it doesn't really make sense. I hope you can clear it up a bit.
     
  8. doc3232

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    Ok, 3/2 and 2/3 are not the best numbers to visualize, why not change it?

    How about double, so 10 workers finish in 5 mins, what if you doubled the workers.
    if you double the speed then you must half the time, hence 2.5 mins.
    Same concept with 3/2 and 2/3.
    Never bother with equations, they WILL confuse the best of us.
    Just use logic and if your not sure about something then make up your own numbers to confirm your thought process.
    Hope that clears it up.
     
  9. sl2obel2ts

    sl2obel2ts i like tomatoes

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    or...
    25 * 5 = 125
    125 = (25+5/6*15)*X
    solve for X
    X = 10/3
    Answer: 5 - 10/3 = 5/3
     
  10. Streetwolf

    Streetwolf Ultra Senior Member
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    n people * t months = 1 complete job.
    (3/2)n people * t months = (3/2) complete job.

    You want to keep the same # of people and only do 1 complete job so the only thing to do is multiply the time by (2/3).

    I know this isn't a great formula but it should help you visualize what's going on a bit better.

    ====

    Another way:

    n workers do 1 complete job in 5 months, so 1 worker does (1/n) complete job in 5 months, and thus (1/5n) complete job in 1 month. Now let's say you have (3/2)n workers. In 1 month they would do (3/10) the job --> (3/2)n * (1/5n). But you want a full job done. So 1 / (3/10) = 10/3 --> this represents the # of times they need to complete (3/10) of the complete job. Thus you need 10/3 months for (3/2)n workers to finish 1 complete job.
     
  11. Hugh Mannity

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    Nice and concise.
     

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