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

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It takes 6 beavers 10 hours to build a certain dam, working at a unifo  [#permalink]

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18 Nov 2015, 00:45
10
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:32) correct 34% (02:58) wrong based on 199 sessions

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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

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Re: It takes 6 beavers 10 hours to build a certain dam, working at a unifo  [#permalink]

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23 May 2017, 16:17
4
1
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.

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Re: It takes 6 beavers 10 hours to build a certain dam, working at a unifo  [#permalink]

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18 Nov 2015, 01:05
2
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

[color=#0000ff]Each beaver can build 1/60 dam per hour
=> From 12 to 6PM: 6 beavers can build 1/60 * 6 * 6 = 6/10 dam

From the next 3 hours: 7/60+8/60+9/60 = 4/10 dam is built more

=> Total hours: 9 => Ans: E
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Re: It takes 6 beavers 10 hours to build a certain dam, working at a unifo  [#permalink]

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18 Nov 2015, 01:56
1
Number of man hours required = 6*10 = 60.
6 workers work for 6 hrs --> Number of man hours completed = 6*6 = 36
Man hours remaining = 60 - 36 = 24
Effort for the next 3 hours = 7 + 8 + 9 = 24. Work gets completed at 9.00 PM

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Re: It takes 6 beavers 10 hours to build a certain dam, working at a unifo  [#permalink]

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18 Nov 2015, 11:44
4
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

Let the total work be 60 units

6 beavers take 10 hours for 60 units of work OR
60 Bh are needed for 60 units of work OR
1BH will be needed for 1 unit of work OR
1 beaver will take 1 hour to complete 1 unit of work

6 Beavers are employed for 6 hours ( From 12 pm - 6 pm ) , so they will complete 36 units of work

After 6 PM - 7 Beavers are employed for 1 hour so they will complete 7 units , total work completed is 43 units
After 7 Pm - 8 Beavers are employed for 1 hour so they will complete 8 units , total work completed is 51 units
After 8 Pm - 9 Beavers are employed for 1 hour so they will complete 9 units , total work completed is 60 units

Thus at 9 PM the work will be completed !!
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It takes 6 beavers 10 hours to build a certain dam, working at a unifo  [#permalink]

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20 Nov 2015, 11:22
1
it takes (6)(10)=60 beaver hours to build dam
(6)(6)=36 beaver hours completed from noon to 6:00pm
60-36=24 beaver hours remaining at 6:00pm
t=time required
ratio of cumulative beaver hours to time=(t+13)/2
24/t=(t+13)/2
t=3 hours
9:00pm
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Joined: 09 Jun 2015
Posts: 92
Re: It takes 6 beavers 10 hours to build a certain dam, working at a unifo  [#permalink]

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18 Mar 2016, 22:18
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

6 beavers can complete in 6 hours 36/60 work
at the end of 7 p.m 36/60 + 7/60
at the end of 8 36/60 + 7/60 + 8/60
at the end of 9 60/60; the work will be completed.
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Re: It takes 6 beavers 10 hours to build a certain dam, working at a unifo  [#permalink]

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19 Mar 2016, 22:01
Vyshak wrote:
Number of man hours required = 6*10 = 60.
6 workers work for 6 hrs --> Number of man hours completed = 6*6 = 36
Man hours remaining = 60 - 36 = 24
Effort for the next 3 hours = 7 + 8 + 9 = 24. Work gets completed at 9.00 PM

Got the same answer with a different approach -

Rate of 1 beaver = 1/60
Amount of work done by 6 beavers till 6 pm (in 6 hours) = 6/60 *6 = 6/10
Amount of work left = 4/10
No. of beavers working between 6 - 7pm = 7
Hence, the amount of work done between 6 - 7 = 7/60
and between 7-8 = 8/60
and between 8-9 = 9/ 60
Adding these 3 we get 4/10 (which was the amount of work left after 6 pm)
Hence the work gets done at 9.

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Re: It takes 6 beavers 10 hours to build a certain dam, working at a unifo  [#permalink]

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17 Jun 2018, 05:29
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Re: It takes 6 beavers 10 hours to build a certain dam, working at a unifo &nbs [#permalink] 17 Jun 2018, 05:29
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