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It takes 6 technicians a total of 10 hours to build and

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It takes 6 technicians a total of 10 hours to build and [#permalink] New post 12 Apr 2010, 04:41
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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. 7:30 PM
B. 7:45 PM
C. 8:00 PM
D. 9:00 AM
E. 10:00 PM
[Reveal] Spoiler: OA

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Last edited by Bunuel on 09 Feb 2012, 11:38, edited 1 time in total.
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Re: Work Rate Problem [#permalink] New post 12 Apr 2010, 06:20
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Ans: C

6Techs can complete the job in 10 hours.
6 Techs can do 1/10 job in 1 hour
1 Tech can do 1/(6*10) = 1/60 job in 1 hour.

Now 6 techs worked from 11.00Am tp 5.00PM means they worked for 6 hours.
6Techs worked for 6 hours = 6/10 job completed.
From 5.00 PM to 6.00 Pm a tech is added, so
7 Techs worked for 1 hour = 7/60 job
Total job completed at 6.00PM is = 6/10+7/60 = 43/60 job done.

From 6.00 PM to 7.00 Pm a tech is added, so
8 Techs worked for 1 hour = 8/60 job
Total job completed at 7.00PM is = 43/60 + 8/60 = 51/60 job done.

From 7.00 PM to 8.00 Pm a tech is added, so
9 Techs worked for 1 hour = 9/60 job
Total job completed at 7.00PM is = 51/60 + 9/60 = 60/60 job done. Job is COMPLETE.

Job is complete at 8.00PM.
The total number of hours is 9 hours.
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Re: Work Rate Problem [#permalink] New post 12 Apr 2010, 06:22
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Hussain15 wrote:
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. 7:30 PM
B. 7:45 PM
C. 8:00 PM
D. 9:00 AM
E. 10:00 PM


To complete the job 6*10=60 man/hours are needed. By 5:00 PM 6*6=36 man/hour done. 24 is left.

5:00 PM - 6:00 PM 7 man/hour;
6:00 PM - 7:00 PM 8 man/hour;
7:00 PM - 8:00 PM 9 man/hour.

7+8+9=24.

Answer: C.
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Re: Work Rate Problem [#permalink] New post 12 Apr 2010, 06:38
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Re: It takes 6 technicians a total of 10 hours to build and [#permalink] New post 30 May 2013, 04:09
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Re: It takes 6 technicians a total of 10 hours to build and [#permalink] New post 13 Jun 2013, 18:45
This is how I approach it:
Because 6 men started at 11am and the addition of another man occurs after 5. Therefore, the amount of work done by 5pm will be = (1/10)X(17-11)= 6/10
The remaining work will thus be = 4/10

(1/10)t+(1/60)[t+(t+1)+...+(t+n)]=(4/10)
(1/10)t+(1/60)[Summation formula: ((tX(t+1))/2)]=4/10

Because t cannot be negative; therefore t=3
3+5=8

Could someone please verify that this method will work for any rate question presented. Thanks.
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Re: It takes 6 technicians a total of 10 hours to build and [#permalink] New post 28 Jun 2013, 11:58
6 person can complete the job in 10 hours.
Rate of work per person per hour = x
W=R*T
1=6x*10
x=1/60

Work done by 6 persons for 6 hours at rate of (1/60)=
6*6*(1/60) = 6/10

Remaining Work = 1-6/10 = 4/10

4/10 = Y(1/60)

Y=24; at 5 pm no of persons were 7, at 6pm: 8, at 7pm :9persons, 7+8+9=24

Answer C

it took 3 hours after 5pm, to complete the task.
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Re: It takes 6 technicians a total of 10 hours to build and [#permalink] New post 28 Jun 2013, 19:12
Hussain15 wrote:
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. 7:30 PM
B. 7:45 PM
C. 8:00 PM
D. 9:00 AM
E. 10:00 PM



We should never, everrr make questions too complicated to infer and solve...
6 tech total of 10 hours... let me assume total of 60 units of work...
1 tech in 1 hr does 1 unit of work.....

11:00 am to 5:pm - 6 hours
so, total work done by 6 tech in 6 hrs will be 36 unit. ( 6*6)
now a new person gets added every hour after 5:00PM

11:00-5:00 - 36 unit
5:00-6:00 - 7 unit ( 6 tech were doing 6 unit in 1 hr, now since a new person has been added, the work increases to 7 unit)
6:00-7:00 - 8 unit ( another guy added)
7:00-8:00- 9 unit ( another guys added making total 9 person in the work field)

36+7+8+9 = 60.


so by 8:00PM 60 units of work was completed by the group....

Bingo..!!!!
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Re: It takes 6 technicians a total of 10 hours to build and [#permalink] New post 29 Jun 2013, 03:50
Hussain15 wrote:
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. 7:30 PM
B. 7:45 PM
C. 8:00 PM
D. 9:00 AM
E. 10:00 PM


1. Originally 6 people work for 60 man hours
2. Additional people work for 6 man hours
3. So to complete the same task since the same man hours is taken , the original 6 people work for 6 man hours less. i.e., they work for 60-6=54 man hours i.e., they work for 9 hours each
4 . In other words if they start the task at 11 A.M , they complete the task at 8:00 PM

The answer is choice C.
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Last edited by SravnaTestPrep on 17 Aug 2013, 03:23, edited 2 times in total.
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Re: Work Rate Problem [#permalink] New post 17 Aug 2013, 02:52
Bunuel wrote:
Hussain15 wrote:
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. 7:30 PM
B. 7:45 PM
C. 8:00 PM
D. 9:00 AM
E. 10:00 PM


To complete the job 6*10=60 man/hours are needed. By 5:00 PM 6*6=36 man/hour done. 24 is left.

5:00 PM - 6:00 PM 7 man/hour;
6:00 PM - 7:00 PM 8 man/hour;
7:00 PM - 8:00 PM 9 man/hour.

7+8+9=24.

Answer: C.


Makes me giggle how Bunuel always finds a simple yet understood solution! Though first I struggle to understand the problem and the previous posters' solutions!
Thanks Bunuel!
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Re: It takes 6 technicians a total of 10 hours to build and [#permalink] New post 17 Aug 2013, 03:38
Hussain15 wrote:
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. 7:30 PM
B. 7:45 PM
C. 8:00 PM
D. 9:00 AM
E. 10:00 PM


6man,
10 hours = 1 full work
6 hours = 3/5 work done. due = 1- 3/5 = 2/5

6 men 10 hours
so 7 men 60/7 hours to complete a job

so, 7 men 1 hour = 7/60
8 men 1 hour = 8/60
9 men 1 hour = 9/60
..........................................
+ 3 hours = 24/60 = 2/5 parts of total works.

so 5+3 = 8pm (Answer)
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Re: It takes 6 technicians a total of 10 hours to build and [#permalink] New post 25 Sep 2013, 21:03
Man * Days * hours = Work done

6 people * 10 hours = 60 units

6 people * (11AM to 5 PM) 6 hours = 36

Work left 60-36 = 24

5-6 : 7 people = 7 units
6-7 : 8 people = 8 units
7-8: 9 people = 9 units
Total = 24 units

hence 8PM
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Re: It takes 6 technicians a total of 10 hours to build and [#permalink] New post 20 Nov 2013, 09:23
Hussain15 wrote:
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. 7:30 PM
B. 7:45 PM
C. 8:00 PM
D. 9:00 AM
E. 10:00 PM


Can someone explain how this fits into the standard w=r*t formula? I feel like that learning that formula was useless, because every time I try and apply it to one of these problems, it's wrong.

"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?"

I tried this: If the rate of a technician is \frac{1}{T}, and you have 6 technicians working from 9-5, then their hourly rate should be 6/T, so using w=r*t
w=8*\frac{6}{t}, so W=\frac{48}{T}. But then what do I do after that?
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Re: It takes 6 technicians a total of 10 hours to build and [#permalink] New post 24 Dec 2013, 12:14
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Hussain15 wrote:
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. 7:30 PM
B. 7:45 PM
C. 8:00 PM
D. 9:00 AM
E. 10:00 PM


So we need 60 hours men to finish the work
6 technitians will work for 6 hours hence they will do 36 hours. We now have 24 hours men left to complete
At 6pm - 7 hours men = 24 - 7 = 17
At 7pm - 8 hours men= 17-8 = 9
At 8pm- 9 hours men = Job Done

Hence answer is (C)

Hope it helps
Cheers!
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Re: It takes 6 technicians a total of 10 hours to build and   [#permalink] 24 Dec 2013, 12:14
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