A contractor estimated that his 10-man crew could complete

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