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what is the easiest way to do these kinda problems.. It

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Senior Manager
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what is the easiest way to do these kinda problems.. It [#permalink] New post 08 Feb 2004, 00:02
what is the easiest way to do these kinda problems..

It takes 6 technicians a total of 10 hours to build and program a new server from Direct Computer, with each working at the same rate. If six technicians start to build the server at 11:00 AM, and one technician per hour is added beginning at 5:00 PM, at what time will the server be complete?

A) 6:40 PM

B) 7:00 PM

C) 7:20 PM

D) 7:40 PM

E) 8:00 PM
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 [#permalink] New post 08 Feb 2004, 02:13
The job is 60 tech/hours. From 11.00 till 5.00 you have 6 hours or the 6 tech have done 6x6=36/60 of the job. Next hour you have 7 people working , as for 1 h. these people will do 7/60 of the job. You go further for 8 and 9 hour. At the end 36/60+7/60+8/60+9/60=60/60 or at 8.00 job will be done
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 [#permalink] New post 08 Feb 2004, 06:46
from 11 to 5 there are 6 hours so the 6 workes would have completed
0.6 job. Remaining os 0.4
Every hour 6 workers do 0.1 job so for n hours after 5 they would have done 0.1 * n job
Since each worker is added every hour we have
1/60 + 2/60 + 3/60 ..... n/60 = 1/60 * n(n+1)/2
so
0.1 * n + 1/60 * n(n+1)/2 = 0.4 job
12n + n^2+n = 48
or n^2+13n-48 = 0 n = 3
The work will be completed after 3 hours from 5 PM = 8 PM
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 [#permalink] New post 08 Feb 2004, 14:38
Ans: E

Official explanation::
6 technicians take 10 hours to build the computer, meaning that it takes 60 worker-hours to build the server. Thus, 1 worker for 1 hour can build 1/60th of the server. The problem then says that 6 technicians begin work at 11:00 AM and work until 5:00 PM. In that six-hour time, 6 technicians should have put up 36/60ths. Then, from 5:00-6:00 PM, 7 technicians are working, adding 7 more 60ths for a total of 43 at 6:00 PM. From 6:00-7:00 PM, 8 technicians are working, adding 8 more 60ths for a total of 51 at 7:00 PM, and from 7:00 - 8:00 PM, 9 technicians are working, adding 9 more components to finish the server with 60 components at 8:00 p.m.


Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

  [#permalink] 08 Feb 2004, 14:38
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