It takes 6 beavers 10 hours to build a certain dam, working

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

Given, that it takes 6 beavers 10 hours to build a certain dam, we need 6*10 = 60 man-hours to complete the dam. Or, in 1 man-hour 1/60 dam is completed.

From 12 noon to 6 pm, in 6 hours, 6 beavers worked or contributed 6*6 = 36 man-hours. This way, 36/60 = 3/5 part of the dam is completed and 1 – 3/5 = 2.5 part of the dam is remaining to be completed.

Since by 6 pm, at every interval of one hour, one beaver is added, we have to compute at what time the dam is completed. Let's understand this at 7 pm, 8 pm, 9 pm, etc.

1. At 7 pm: From 6 to 7 pm, we have 7 weavers, thus 7*(1/60) = 7/60 part of the dam was completed. Thus, part of the dam remaining to be completed at 7 pm = 2/5 – 7/60 = 17/60 part

2. At 8 pm: From 7 to 8 pm, we have 8 weavers, thus 8*(1/60) = 2/15 part of the dam was completed. Thus, part of the dam remaining to be completed at 8 pm = 17/60 – 2/15 = 9/60 part

2. At 9 pm: From 8 to 9 pm, we have 9 weavers, thus 9*(1/60) part of the dam was completed. Thus, part of the dam remaining to be completed at 9 pm = 9/60 – 9/60 = 0. Dam is completed by 9 pm.

The correct answer: [spoilerE][/spoiler]

Hope this helps!

-Jay
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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