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A contractor estimated that his 10-person crew could complete a construction project in 110 days if there were no rain delays. (Assume the crew does not work on rainy days and that rain is the only factor preventing the crew from working). However, on day 61, after having experienced a total of 5 days of rain in the previous days, the contractor hired 6 additional workers and managed to finish the project early. If the project was completed in 100 days, how many rainy days occurred after day 60?
A. 4
B. 5
C. 6
D. 7
E. 8
A. 4
B. 5
C. 6
D. 7
E. 8
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16 Jan 2012, 13:07
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Official Solution:
A contractor estimated that his 10-person crew could complete a construction project in 110 days if there were no rain delays. (Assume the crew does not work on rainy days and that rain is the only factor preventing the crew from working). However, on day 61, after having experienced a total of 5 days of rain in the previous days, the contractor hired 6 additional workers and managed to finish the project early. If the project was completed in 100 days, how many rainy days occurred after day 60?
A. 4
B. 5
C. 6
D. 7
E. 8
Given: A 10-person crew requires 110 days to complete the construction project.
"On day 61, after experiencing 5 days of rain...": Since there were 5 days of rain out of the first 60 days, the crew must have been working for 55 days, thus completing half of the job, with the other half remaining (55 days of work for the 10-person crew).
Subsequently, the contractor hired "6 additional workers": This increased the construction speed by 1.6 times. Therefore, the new 16-person crew would require \(\frac{55}{1.6} \approx 34.4\) days to complete the construction. However, after the additional workers were hired, the project was completed in \(100-60=40\) days. As a result, there must have been 5 rainy days during this period. (The crew needed MORE than 34 days to finish the job, so if there had been 6 rainy days, they wouldn't have been able to complete the project within 100 (40) days.)
Answer: B
A contractor estimated that his 10-person crew could complete a construction project in 110 days if there were no rain delays. (Assume the crew does not work on rainy days and that rain is the only factor preventing the crew from working). However, on day 61, after having experienced a total of 5 days of rain in the previous days, the contractor hired 6 additional workers and managed to finish the project early. If the project was completed in 100 days, how many rainy days occurred after day 60?
A. 4
B. 5
C. 6
D. 7
E. 8
Given: A 10-person crew requires 110 days to complete the construction project.
"On day 61, after experiencing 5 days of rain...": Since there were 5 days of rain out of the first 60 days, the crew must have been working for 55 days, thus completing half of the job, with the other half remaining (55 days of work for the 10-person crew).
Subsequently, the contractor hired "6 additional workers": This increased the construction speed by 1.6 times. Therefore, the new 16-person crew would require \(\frac{55}{1.6} \approx 34.4\) days to complete the construction. However, after the additional workers were hired, the project was completed in \(100-60=40\) days. As a result, there must have been 5 rainy days during this period. (The crew needed MORE than 34 days to finish the job, so if there had been 6 rainy days, they wouldn't have been able to complete the project within 100 (40) days.)
Answer: B
08 Jan 2011, 12:33
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rtaha2412
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.)
Answer: B.
