Question

140 workers started working a job that according to plan should last 100 days, after 15, 35 more workers came. How long will it take them to finish the job, and how long did the whole job last?

A. 15 days to finish, 115 days total
B. 20 days to finish, 120 days total
C. 25 days to finish, 105 days total
D. 30 days to finish, 110 days total

Answer 1

The total number of workers is 175. The man-days for the whole job is 31,500. It will take 30 days for the workers to finish the job and the total duration of the job is 110 days.

Step-by-step explanation:

To find out how long it will take the workers to finish the job and how long the whole job lasted, we first need to calculate the total number of workers. Initially, there were 140 workers, and then an additional 35 workers joined. Therefore, the total number of workers is 140 + 35 = 175.

Next, we can use the concept of man-days to determine the time required to finish the job. The man-days is calculated by multiplying the number of workers by the number of days. In this case, the initial 140 workers worked for 100 days, and the additional 35 workers joined after 15 days. So, the man-days for the initial period would be 140 workers x 100 days = 14,000 man-days.

For the second period, we have 175 workers x (100 - 15) days = 17,500 man-days.

The total man-days for the whole job would be the sum of the man-days for the initial and second periods, which is 14,000 + 17,500 = 31,500 man-days.

To find out how long it will take the workers to finish the job, we can divide the total man-days by the total number of workers. So, 31,500 man-days / 175 workers = 180 days.

Therefore, the correct answer is D. 30 days to finish, 110 days total.