Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $8$ days earlier. If the job needs to completed $28$ days earlier, how many additional workers should be hired?

tomtom Mar 7, 2024

#1**+1 **

Let the time to complete the job with 5 workers = T days

So......the total man-days for the job is 5T

If one additional worker is hired, the man-days for the job is 6 (T - 8)

So....since the man-days will be the same for the job.....

5T = 6(T - 8)

5T = 6T - 48

48 = T

So the number of man-days to complete the job is 5(48) = 240

So.....to complete the job 28 days earlier

(number of workers needed) * ( 48 - 28) = 240

(number of workers needed) * (20) = 240

number of workers needed = 240 / 20 = 12

So.....(12 - 5) = 7 additional workers should be hired to complete the job 28 days earlier

CPhill Mar 8, 2024