Bunuel wrote:

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

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 a dam. So 1 - 3/5 = 2/5 of a 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 a dam by 7 PM. So 2/5 - 7/60 = 24/60 - 7/60 = 17/60 of a 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 a dam by 8 PM. So 17/60 - 8/60 = 9/60 of a dam 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 a dam by 9 PM. This completes the 9/60 of a dam that remained to be completed at 8 PM. Therefore, they complete the dam at 9 PM.

Answer: E

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