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

Let the rate for each technician = 1 unit per hour, implying that the rate for 6 technicians = 6 units per hour.
Since 6 technicians take 10 hours to produce a server, the total job = (rate for 6 technicians)(number of hours) = 6*10 = 60 units.

From 11am to 5pm -- a total of 6 hours -- the amount of work produced by 6 technicians = (rate for 6 technicians)(number of hours) = 6*6 = 36 units.
Remaining work = 60-36 = 24 units.

Starting at 5pm, one worker is added every hour, implying that the rate increases every hour by 1 unit.
Thus:
From 5-6pm, 7 units are produced.
Remaining work = 24-7 = 17 units.
From 6-7pm, 8 units are produced.
Remaining work = 17-8 = 9 units.
From 7-8pm, 9 units are produced.
Remaining work = 9-9 = 0 units.

Since no units remain, the server is finished by 8pm.

The correct answer is C.

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