lheiannie07 wrote:It takes 6 technicians a total of 10 hours to build and program a new server from Direct Computer, with each working at the same rate. If six technicians start to build the server at 11:00 AM, and one technician per hour is added beginning at 5:00 PM, at what time will the server be complete?
A. 7:30 PM
B. 7:45 PM
C. 8:00 PM
D. 9:00 AM
E. 10:00 PM
We are given that six technicians can complete a job in 10 hours. Since rate = work/time, the rate of the 6 technicians is 1/10. Thus, the rate of 1 technician is (1/10)/6 = 1/60.
We see that 6 technicians work from 11:00 AM to 5:00 PM or 6 hours. Since rate x time = work, those technicians complete 1/10 x 6 = 6/10 = 3/5 of the job.
If another technician is added to the job at 5:00 PM, the new rate for the technicians is (1/60) x 7 = 7/60 and thus all 7 complete 7/60 of the job in that hour.
Thus, 3/5 + 7/60 = 36/60 + 7/60 = 43/60 of the job is complete
If another technician is added to the job at 6:00 PM, the new rate for the technicians is (1/60) x 8 = 8/60 and thus all 8 complete 8/60 of the job in that hour.
Thus, 43/60 + 8/60 = 51/60 of the job is complete
If another technician is added to the job at 7:00 PM, the new rate for the technicians is (1/60) x 9 = 9/60 and thus all 9 complete 9/60 of the job in that hour.
Thus, 51/60 + 9/60 = 60/60 of the job is complete at 8:00 PM.
Alternate Solution:
Since it takes 6 technicians a total of 10 hours to complete the server, we see that the entire job will require 60 labor-hours for completion.
For the 6 hours from 11 am to 5 pm, the 6 technicians will contribute 36 labor-hours to the task.
From 5 pm to 6 pm, the 7 technicians will contribute 7 more labor-hours, for a subtotal of 43 labor-hours.
From 6 pm to 7 pm, the 8 technicians will contribute 8 more labor-hours, for a subtotal of 51 labor-hours.
From 7 pm to 8 pm, the 9 technicians will contribute 9 more labor-hours, for a total of 60 labor-hours, thus completing the entire job at 8 p.m.
Answer:
C
