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Math Help - Solve this prob!

  1. #1
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    Solve this prob!

    Bob calculated that his 8 professional workers would take 15 hours each to pack a few parcels.

    If all the workers work at the same rate, how long would it take 12 workers to pack all the parcels.

    I somehow got 10. I dunno if it is right.

    Can someone not necessarily tell me the answer but point me in the right direction?
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  2. #2
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    Quote Originally Posted by jgv115 View Post
    Bob calculated that his 8 professional workers would take 15 hours each to pack a few parcels.

    If all the workers work at the same rate, how long would it take 12 workers to pack all the parcels.

    I somehow got 10. I dunno if it is right.

    Can someone not necessarily tell me the answer but point me in the right direction?
    Solve...

     <br />
\frac{15}{8}=\frac{x}{12}<br /> <br />
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  3. #3
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    Yea I did that already

    x = 22.5

    22.5 hours...

    The number of hours should be lower than 15 hours because there are more people working on it...
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  4. #4
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    Quote Originally Posted by jgv115 View Post
    Bob calculated that his 8 professional workers would take 15 hours each to pack a few parcels.
    If all the workers work at the same rate, how long would it take 12 workers to pack all the parcels.
    Total number of man hours needed to complete the packing is 8*15.
    To complete the same work, 12 workers take x hours each. So
    8*15 = 12*x.
    Solve for x.
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  5. #5
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    Yes, I should read more closely.

    You are saying 10 hours because you have 50% more workers (4 extra out of a new total of 12 is one third) and therefore time taken should be cut by one third.
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  6. #6
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    mm ok.

    In that case:

    12 workers are joined by 8 new workers. New workers work at half the rate of normal workers. How long would it take to pack the boxes?

    Here's what I did: 8 new workers is equivalent to 4 "normal" workers.

    So  15*8 = 16 * x

     120 = 16x

     x= 7.5

    Is that all good?
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  7. #7
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    Yes. You are right.
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  8. #8
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    (remember that training workers that half the time of normal workers)

    Some normal workers and 6 training workers would have taken 12 hours to complete the job. How many normal workers were there?

    We know the job is 120.

    Let x be the number of normal workers:

    120= (x+3) * 12

     x= 7

    Is this all good?

    Last one:

    If after 2.5 hours, two normal workers and all training workers had to leave. How much longer would the remaining workers take to finish packing than if no one had left.

    So basically I worked out a rate.

    In 12 hours, 10 normal workers (7 normal + 6 training) would complete 120. So if they were given only 2.5 hours then...

     \frac {120}{12} = \frac{x}{2.5} x = how much work was done.

     x= 25

    So the remaining work is 120-25 which is 95. There are 5 (7-2) normal workers left and no training workers (all left)

     95 = 5x where x = the number of hours it takes

     x= 19

    So altogether the workers took 21.5 hours to complete the task when some workers left.

    It took 12 hours for 10 workers to do the job.

    So 21.5 - 12 = 9.5

    So it would take 9.5 hours longer.

    Is this correct? :S
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  9. #9
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    Yes, I think so. I got the same answer as you
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