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# A contractor estimated that his 10-man crew could complete

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A contractor estimated that his 10-man crew could complete [#permalink]  16 Jan 2012, 09:19
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A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

A. 4
B. 5
C. 6
D. 7
E. 8
[Reveal] Spoiler: OA

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Re: A contractor estimated that his 10-man [#permalink]  16 Jan 2012, 12:07
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Expert's post
manalq8 wrote:
A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

A. 4
B. 5
C. 6
D. 7
E. 8

Given: 10-man crew needs 110 days to complete the construction.

"On the 61-st day, after 5 days of rain ..." --> as it was raining for 5 days then they must have bee working for 55 days thus completed 1/2 of the job, 1/2 is left (55 days of work for 10 men).

Then contractor "hired 6 more people" --> speed of construction increased 1.6 times, so the new 16-man crew needed 55/1.6=~34.4 days to complete the construction, but after they were hired job was done in 100-60=40 days --> so 5 days rained. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100(40) days.)

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Re: A contractor estimated that his 10-man crew could complete [#permalink]  17 Jan 2012, 02:16
Bunnel - Could you please explain the step
"Then contractor "hired 6 more people" --> speed of construction increased 1.6 times, so the new 16-man crew needed 55/1.6=~34.4 days"
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Re: A contractor estimated that his 10-man crew could complete [#permalink]  17 Jan 2012, 02:41
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subhajeet wrote:
Bunnel - Could you please explain the step
"Then contractor "hired 6 more people" --> speed of construction increased 1.6 times, so the new 16-man crew needed 55/1.6=~34.4 days"

10 men need 55 days to complete a job. How many days does 20 men need to complete the same job? In 55/2 days (the rate of 20 men group is twice the rate of 10 men group).

Similarly, if 10 men need 55 days to complete a job, 16 men (10*1.6) will need 55/1.6 days to complete the job (the rate of 16 men group is 1.6 times greater than the rate of 10 men group).

Or: there was 10*55=550 man-days of work left which can be done by 16 men in 550/16=~34.4 days.
Refer to two-consultants-can-type-up-a-report-126155.html for theory on work problems and practice questions.

Hope it helps.
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Re: A contractor estimated that his 10-man crew could complete [#permalink]  17 Jan 2012, 02:47
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manalq8 wrote:
A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

4
5
6
7
8

You can also look at this problem in terms of units of work.

10 people can finish the work in 110 days so there are 1100 units of work (1 unit done by 1 man in 1 day)
10 men worked for 55 days and did 10*55 = 550 units (since it rained for 5 days so day 56th to day 60th were all washed out). Now 550 units are left. [Mind you, it is an assumption that there was no rain in the first 55 days. Ideally, the question should have explicitly stated it.)

Now there are 16 people to do 550 units of work. Work will be done in 550/16 = 34.4 days i.e. 35 days are needed.
After 60th day, we have total 40 days. Out of these, 35 are needed so it must have rained on 5 days.
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Re: A contractor estimated that his 10-man crew could complete [#permalink]  17 Jan 2012, 02:51
1
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Bunuel wrote:
subhajeet wrote:
Bunnel - Could you please explain the step
"Then contractor "hired 6 more people" --> speed of construction increased 1.6 times, so the new 16-man crew needed 55/1.6=~34.4 days"

10 men need 55 days to complete a job. How many days does 20 men need to complete the same job? In 55/2 days (the rate of 20 men group is twice the rate of 10 men group).

Similarly, if 10 men need 55 days to complete a job, 16 men (10*1.6) will need 55/1.6 days to complete the job (the rate of 16 men group is 1.6 times greater than the rate of 10 men group).

Or: there was 10*55=550 man-days of work left which can be done by 16 men in 550/16=~34.4 days.
Refer to two-consultants-can-type-up-a-report-126155.html for theory on work problems and practice questions.

Hope it helps.

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Re: A contractor estimated that his 10-man crew could complete [#permalink]  20 Jul 2012, 09:45
VeritasPrepKarishma wrote:
manalq8 wrote:
A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

4
5
6
7
8

You can also look at this problem in terms of units of work.

10 people can finish the work in 110 days so there are 1100 units of work (1 unit done by 1 man in 1 day)
10 men worked for 55 days and did 10*55 = 550 units (since it rained for 5 days so day 56th to day 60th were all washed out). Now 550 units are left. [Mind you, it is an assumption that there was no rain in the first 55 days. Ideally, the question should have explicitly stated it.)

Now there are 16 people to do 550 units of work. Work will be done in 550/16 = 34.4 days i.e. 35 days are needed.
After 60th day, we have total 40 days. Out of these, 35 are needed so it must have rained on 5 days.

Thanks for letting kw the easy method.
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Re: A contractor estimated that his 10-man crew could complete [#permalink]  20 Jul 2012, 11:22
I thought of the problem in units of work. The total project needed 1100 units of work. 550 of these units were completed by the 55th day (10 x 55). It rained on the 56th, 57th, 58th, 59th, and 60th day. On the 61st day, the contractor hired 6 more laborers thus bringing the total laborer population to 16. With 550 units of work left, these 16 laborers should have completed the remaining work in 34.375 days.

Here's where I went wrong. I added 34.375 to 61 to bring total days needed (assuming no rain after the 60th) to 95.375 (essentially 96 days of work). However, this would imply only 4 days of rain since the project actually took 100 days to complete. I believe I went wrong in adding the 34.375 to 61 instead of 60 since by doing the former I didn't credit them for one day of work. Could someone confirm this?

Thank you.
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Re: A contractor estimated that his 10-man crew could complete [#permalink]  20 Jul 2012, 11:42
Club909 wrote:
I thought of the problem in units of work. The total project needed 1100 units of work. 550 of these units were completed by the 55th day (10 x 55). It rained on the 56th, 57th, 58th, 59th, and 60th day. On the 61st day, the contractor hired 6 more laborers thus bringing the total laborer population to 16. With 550 units of work left, these 16 laborers should have completed the remaining work in 34.375 days.

Here's where I went wrong. I added 34.375 to 61 to bring total days needed (assuming no rain after the 60th) to 95.375 (essentially 96 days of work). However, this would imply only 4 days of rain since the project actually took 100 days to complete. I believe I went wrong in adding the 34.375 to 61 instead of 60 since by doing the former I didn't credit them for one day of work. Could someone confirm this?

Thank you.

You are right. You simply took away one work day. The 61st day of the project was a work day, in fact the first day when the extended team of 16 took over the job.
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Re: A contractor estimated that his 10-man crew could complete [#permalink]  20 Jul 2012, 18:19
Expert's post
Club909 wrote:
I thought of the problem in units of work. The total project needed 1100 units of work. 550 of these units were completed by the 55th day (10 x 55). It rained on the 56th, 57th, 58th, 59th, and 60th day. On the 61st day, the contractor hired 6 more laborers thus bringing the total laborer population to 16. With 550 units of work left, these 16 laborers should have completed the remaining work in 34.375 days.

Here's where I went wrong. I added 34.375 to 61 to bring total days needed (assuming no rain after the 60th) to 95.375 (essentially 96 days of work). However, this would imply only 4 days of rain since the project actually took 100 days to complete. I believe I went wrong in adding the 34.375 to 61 instead of 60 since by doing the former I didn't credit them for one day of work. Could someone confirm this?

Thank you.

Think of it this way: 60 days are accounted for. From the 61st day to the 100th day, there are 40 days. You need 35 of these to complete the work so you are left with 5 days.
When you add 35 to 61, you are saying that 61 days are accounted for but that is not the case.
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Re: A contractor estimated that his 10-man crew could complete [#permalink]  14 Nov 2012, 06:30
$$\frac{10}{m}=\frac{1}{110}$$
$$rate=\frac{1}{1100}$$

10 men worked for 60-5=55 days...

$$\frac{10}{1100}(55)=\frac{55}{110}=\frac{1}{2}$$

How many remaining days required to finish with 16 men?

$$\frac{16}{1100}(t)=1/2==> t=34.3 days$$ is needed to finish the remaining work

To finish in 100 days or with the 40 days remaining, it should not rain for more than 5 days.

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Re: A contractor estimated that his 10-man [#permalink]  05 Jan 2013, 01:26
Bunuel wrote:
manalq8 wrote:
A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

A. 4
B. 5
C. 6
D. 7
E. 8

Given: 10-man crew needs 110 days to complete the construction.

"On the 61-st day, after 5 days of rain ..." --> as it was raining for 5 days then they must have bee working for 55 days thus completed 1/2 of the job, 1/2 is left (55 days of work for 10 men).

Then contractor "hired 6 more people" --> speed of construction increased 1.6 times, so the new 16-man crew needed 55/1.6=~34.4 days to complete the construction, but after they were hired job was done in 100-60=40 days --> so 5 days rained. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100(40) days.)

Hi,

Estimated time = 110 days
actual completed time = 100 days
no work days = 110-100 = 10 days
we are given only rain is a factor because of which no work will be done and it has already rained for 5 days before the 60th. thus 10-5 = 5 more days it will rain after the 60th

why do we have get into work and rates for this?
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Re: A contractor estimated that his 10-man [#permalink]  05 Jan 2013, 01:39
Expert's post
geezer0305 wrote:
Hi,

Estimated time = 110 days
actual completed time = 100 days
no work days = 110-100 = 10 days
we are given only rain is a factor because of which no work will be done and it has already rained for 5 days before the 60th. thus 10-5 = 5 more days it will rain after the 60th

why do we have get into work and rates for this?

It took 100 days to complete the work instead of the estimated 110 because he employed 6 extra people, not because they did not work on those days. The workers actually worked for only 90 days. Out of the 100 days, it rained for 10 days and they worked for the rest of the 90 days. It is just a co-incidence that the extra workforce reduced the working days by 10, the same number of days for which it rained.
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Re: A contractor estimated that his 10-man crew could complete [#permalink]  14 Oct 2013, 11:09
Given 10 men took 110 days.
Total work = 1100 Man Days

Given on the 61-st day, after 5 days of rain, which means the 10 men worked for 55 days and completed:
55 X 10 = 550 Man Days of work.

Remaining work = 1100-550 = 550 Man Days of work.

Problem states that the work was completed early in 100 days by the 16 men.
Assume it rained on x days, so the work was completed in 40-x days
Hence , 16 (40-x)=550
or x ~ 5 days

Hi,
I wanted to understand if the above mentioned step in red is right.
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Re: A contractor estimated that his 10-man crew could complete [#permalink]  14 Oct 2013, 22:49
Expert's post
chechaxo wrote:
Given 10 men took 110 days.
Total work = 1100 Man Days

Given on the 61-st day, after 5 days of rain, which means the 10 men worked for 55 days and completed:
55 X 10 = 550 Man Days of work.

Remaining work = 1100-550 = 550 Man Days of work.

Problem states that the work was completed early in 100 days by the 16 men.
Assume it rained on x days, so the work was completed in 40-x days
Hence , 16 (40-x)=550
or x ~ 5 days

Hi,
I wanted to understand if the above mentioned step in red is right.

Yes, but ensure that you understand how to deal with fractions.

16 (40-x)=550
40 - x = 34.375
x = 5.625
Now will you say it rained for 5 days or 6 days? Note that you will say that it rained for 5 days because the workers needed the extra .375 day to complete the work. If it were to rain on the 6th day too, the workers would not have been able to work on that day and hence the work would not be complete.
The fraction means that on the 100th day, the workers worked i.e. there was no rain but they worked for only a fraction of the day because the work got over.
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Re: A contractor estimated that his 10-man crew could complete   [#permalink] 14 Oct 2013, 22:49
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