BTGmoderatorLU wrote:Source: Princeton Review
It takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If six beavers start to build the same dam at noon, and one beaver per hour is added beginning at 6:00 PM, at what time will the dam be complete?
A. 7:40 PM
B. 8:00 PM
C. 8:20 PM
D. 8:40 PM
E. 9:00 PM
The OA is E
If 6 beavers build a dam in 10 hours, the rate of 6 beavers is 1/10 of a dam per hour and the rate of 1 beaver is (1/10)/6 = 1/60 of a dam per hour.
If 6 beavers start to build a dam at noon, by 6 PM, they will complete 6 x (1/10) = 6/10 = 3/5 of the dam. So 1 - 3/5 = 2/5 of the dam remains to be completed at 6 PM.
At this time, a new beaver joins in; thus, the rate of the 7 beavers is 7 x (1/60) = 7/60 of a dam per hour, and they will complete 7/60 of the dam by 7 PM. So 2/5 - 7/60 = 24/60 - 7/60 = 17/60 of the dam remains to be completed at 7 PM.
At this time, another new beaver joins in; thus, the rate of the 8 beavers is 8 x (1/60) = 8/60 of a dam per hour and they will complete 8/60 of the dam by 8 PM. So 17/60 - 8/60 = 9/60 of thedam remains to be completed at 8 PM.
At this time, yet another new beaver joins in; thus, the rate of the 9 beavers is 9 x (1/60) = 9/60 of a dam per hour, and they will complete 9/60 of the dam by 9 PM. This completes the 9/60 of the dam that remained to be completed at 8 PM. Therefore, they complete the dam at 9 PM.
Alternate Solution:
If it takes 6 beavers 10 hours to build the dam, then a total of 60 beaver-hours is needed to complete the job. From noon to 6 p.m., we have 6 beavers working, so their total hours is 6 x 6 = 36 hours.
From 6 p.m to 7 p.m., 7 beavers work for 1 hour, so the total output since noon is 36 + 7 = 43 hours.
From 7 p.m. to 8 p.m., 8 beavers work for 1 hour, so the total output since noon is now 43 + 8 = 51 hours.
From 8 p.m. to 9 p.m., 9 beavers work for 1 hour, so the total output since noon is now 51 + 9 = 60 hours.
Thus, the dam is completed at 9 p.m.
Answer: E
