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From challenge x A contractor estimated that his 10-man

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From challenge x A contractor estimated that his 10-man [#permalink] New post 04 Nov 2005, 19:52
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From challenge x

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 day that rains and rain is the only factor that deters the crew from working). However, after 5 days of rain, on the 61st day, the contractor hired 6 more workers to finish the construction project ahead of schedule. If the job was completed in 100 days, how many days did it rain during this period?

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 [#permalink] New post 04 Nov 2005, 20:20
6 days ...

10 M will finish the job in 110 days, and it rained for continous 5 day on 61th day ...so 10 M's have worked for inital 55 days....which means they have finished half of the work ..

Now the Remaining work is done by 16 M so time taken = 55*10/16= 550/16 days


tatal time taken = 55 + 550/16 = 89.375 (Actual No of days the men worked)

but the work was finished in 100 days which means

100 = 89+5(Inital days of Rain) + rain after

Rain After = 100 - 94 = 6



8-) 8-) what is OA ....?
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 [#permalink] New post 04 Nov 2005, 20:54
cool_jonny009 wrote:
6 days ...

10 M will finish the job in 110 days, and it rained for continous 5 day on 61th day ...so 10 M's have worked for inital 55 days....which means they have finished half of the work ..

Now the Remaining work is done by 16 M so time taken = 55*10/16= 550/16 days


tatal time taken = 55 + 550/16 = 89.375 (Actual No of days the men worked)

but the work was finished in 100 days which means

100 = 89+5(Inital days of Rain) + rain after

Rain After = 100 - 94 = 6



8-) 8-) what is OA ....?


I think the first rain period is from 56th day to 60th day ...coz on 61th day 16 workers starting the rest of work.
so it should be 55(10 workers' completion)+ 5( first raining period) + 35 (working days by 16 workers) + x ( the other raining days)=100 ---> x=5
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 [#permalink] New post 04 Nov 2005, 21:13
OA is 5 and here's the OE (go get snacks before reading this):

Explanation

The crew has done half the job on the 60th day - they worked for 55 days as it was raining for 5 days. The other half would have taken the same amount of time if it were not for the 6 new workmen hired. They sped up the process by 60%

They would have worked at the rate of 1/55 of work per day for the remaining 55 days, however with the new crew, they did it at the rate of 1.6/55 or 8/275.

So our equation is 8x/275 = 1.
x = 275/8 = 34.375.
So, the new crew finished the job in 35 days, giving us that it was raining 5 more days (35+5) to finally finish the job by the end of the 100th day.

Alternative Explanation:
Before the contractor hired new men 1/2 of the job was completed. It is because the crew worked for 55 days (on 5 days it was raining and the crew didn't work). Suppose, it did not rain after the crew grew to 16. In how many days would this new crew complete the remaining half of the job? As it would have taken 10 men 55 days to complete the job, 16 men would have done it in 1/(1/55*1.6) = 34.375 days or 35 whole days. Therefore, we could expect the job to have been completed by the end of 60 + 35 = 95th day. In reality, it took five days more than that. So, it was raining for 5 days since the addition to the crew. In all, it rained for 10 days since the project started.

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Re: Work PS [#permalink] New post 04 Nov 2005, 21:26
10 people x 110 days = (16 people x 40 days) + (16 people x d days)
(1100 days - 550 days)/16 = d days
d days = 550/16= approx 34 days

so rainy days 40 days - 34 days = 6 days during the period 16 people worked.........
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 [#permalink] New post 04 Nov 2005, 21:29
Oppss!! i should have considerd 34.375 as 35 days ... :x :x :x
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Re: Work PS [#permalink] New post 30 Oct 2011, 09:49
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My approach:
Total work should be done: 10*110=1100
the work done by 10 workers before rain: 10*55=550
the work remained: 1100-550=550

the no. of days needed to complete the task by 16 workers (without rain):
16*days=550
days=34.37=35
So,
55+5+35+X=100
X=5
Re: Work PS   [#permalink] 30 Oct 2011, 09:49
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