SOLUTION: A Foreman needs 14 workers to complete a certain task in 16 days. However, after 8 days, the engineer instructed him to complete the task in following 4 days to allow other teams

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A Foreman needs 14 workers to complete a certain task in 16 days. However, after 8 days, the engineer instructed him to complete the task in following 4 days to allow other teams      Log On


   

Question 1125787: A Foreman needs 14 workers to complete a certain task in 16 days. However,
after 8 days, the engineer instructed him to complete the task in following 4 days to
allow other teams enough time. How many additional workers does the foreman
need to request for?
a. 6
b. 10
c. 9
d. 8
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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A Foreman needs 14 workers to complete a certain task in 16 days.
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r, the rate of one worker
1, one whole job
n, additional workers

14r%2A16=1

highlight_green%28r=1%2F%2814%2A16%29%29


----
However,
after 8 days,
----

Amount of job not yet completed
Half of the job;
1%2F2


----
the engineer instructed him to complete the task in following 4 days. How many additional workers does the foreman
need to request for?
----

highlight_green%28%2814%2Bn%29r%2A4=1%2F2%29
-
14%2Bn=%281%2F2%29%281%2F4%29%281%2Fr%29
n=%281%2F8%29%281%2Fr%29-14
n=%281%2F8%29%2814%2A16%29-14
n=14%2A2-14
highlight%28n=14%29

Answer by ikleyn(52779) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  After working 8 days, the team of 16 workers completes one half of the job; hence, one half of the job remains to do.


2.  If 14 workers complete the job in 16 days,  then 14 workers would complete the remaining half of the job in 8 days.


    Since the requirement is to complete the remaining half of the job in 4 days,

    28 workers are needed for it, in all.


3.  Hence,  28-14 = 14 additional workers should be employed.