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

Question

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

JeffTargetTestPrep · Accepted Answer

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

Abhishek009 · Answer

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 !!

camlan1990 · Answer

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

Kurtosis · Answer

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

Answer: E

gracie · Answer

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

Mathivanan Palraj · Answer

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.

bethebest · Answer

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.

Answer - E

effatara · Answer

This is a more comprehensive approach using the formula for 'sum of an arithmetic series'. This can be applied to solve similar problems where a greater number of hours are needed for completing the work from the point where one worker is added to the workforce every hour. For instance if, say, 19 additional hours are needed to complete the work, the process of step-by-step compilation of the amounts of work done each hour would be time consuming.

By 6:00 pm, the 6 beavers will have completed 3/5 of the work of the dam so 2/5 of work remains to be done. From this point on, 1 beaver is added to the workforce (WF) every hour until the dam is finished.
1 beaver can do 1/60 of the work in 1 hour. Let 'n' be the number of hours needed after 6:00 pm to finish the dam.

The strength of the WF in each of the 1st, 2nd and 'n'th hours are 7, 8 and {7+(n-1)1}** and the corresponding portions of the work done are (1/60)*7, (1/60)*8 and (1/60)*{7+(n-1)1} respectively. 
(** Refer to the formula for the 'n'th term of an Arithmetic Series)
The total portion of work done in 'n' hours = (1/60){7+8+...(n-1)1} = (1/60){n* /2} = (1/60){n(13+n)/2} 
Since the total portion of work completed in 'n' hrs is equal to the remaining (2/5)th:

(1/60){n(13+n)/2} = (2/5)...> n^2+13n-48=0...> n^2 + 16n - 3n - 48 = 0...> n(n+16)-3(n+16)...> (n-3)(n+16)=0...> n=3.

Therefore, 3 hours are needed (after 6:00 pm) to complete - the dam will be finished at 9:00 pm. ANS: E

KarishmaB · Answer

Use units of work - 6 beavers for 10 hrs means 60 units of work are required. From 10 noon to 6 pm, 6 beavers complete 6*6 = 36 units of work. Leftover are 60 - 36 = 24 units of work. In the next few hours, the units of work completed each hour will keep increasing by 1 i.e. 7 units + 8 units + 9 units. These add up to 24 units ( 7 + 8 + 9 = 24) so work will be complete by 9 PM. Answer (E) Here are some work-rate discussions: https://youtu.be/88NFTttkJmA https://anaprep.com/arithmetic-applying ... -concepts/ https://anaprep.com/arithmetic-work-rat ... s-and-all/ https://anaprep.com/arithmetic-avoiding ... work-rate/

bumpbot · Answer

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

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