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Re M0003 [#permalink]
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16 Sep 2014, 00:14
Official Solution:A qualified worker digs a well in 5 hours. He invites 2 apprentices, each working \(\frac{3}{4}\) as fast as the qualified worker and 2 trainees each working \(\frac{1}{5}\) as fast as the qualified worker. If the fiveperson team digs the same well, approximately how much time does the team need to finish the job?A. 1 hour 24 minutes B. 1 hour 34 minutes C. 1 hour 44 minutes D. 1 hour 54 minutes E. 2 hours 14 minutes Follow a basic approach: \(Work=Rate*Time\) \(Q\) is a rate of a qualified worker. \(\frac{3}{4}*Q\)  that of an apprentice. \(\frac{1}{5}*Q\)  that of a trainee. When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+2*(\frac{3}{4}*Q)+2*(\frac{1}{5}*Q))*T\). \(5 = \frac{29}{10}*T\). So, \(T=\frac{50}{29}\) or approximately 1 hour 44 minutes. Answer: C
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Re: M0003 [#permalink]
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29 Nov 2014, 11:19
to get from 50/29 to 1:44 did you just do the division, and get 1.724. from this 1=60min and .724*60min=43.44, or ~44?
Is there a quicker way to do this?
Thanks



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Re: M0003 [#permalink]
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11 Jan 2015, 19:11
JackSparr0w wrote: to get from 50/29 to 1:44 did you just do the division, and get 1.724. from this 1=60min and .724*60min=43.44, or ~44?
Is there a quicker way to do this?
Thanks Convert to 1 hr and 21/29 > compare to 21/28= 3/4 ~ 44 min



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Re: M0003 [#permalink]
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11 Jan 2015, 20:00
How do we know 1:44 stands for 1 hour 44 mins? I got 50/29 and then just blanked out.... thinking all the answers are in ratios as in 1/24, 1/34 and so on.. Bunuel wrote: Official Solution:A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working \(\frac{3}{4}\) as fast and 2 trainees both working \(\frac{1}{5}\) as fast as he. If the fiveperson team digs the same well, how much time does the team need to finish the job? A. 1:24 B. 1:34 C. 1:44 D. 1:54 E. 2:14 Follow a basic approach: \(Work=Rate*Time\)  \(Q\) is a rate of a qualified worker
 \(3\frac{Q}{4}\)  that of an apprentice
 \(\frac{Q}{5}\)  that of a trainee
When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+\frac{3}{2}Q+\frac{2}{5}Q)T\) \(5 = \frac{29}{10}T\) So, \(T=\frac{50}{29}\) or 1:44. Answer: C



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Re: M0003 [#permalink]
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19 Mar 2015, 12:57
Bunuel wrote: Official Solution:A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working \(\frac{3}{4}\) as fast and 2 trainees both working \(\frac{1}{5}\) as fast as he. If the fiveperson team digs the same well, how much time does the team need to finish the job? A. 1:24 B. 1:34 C. 1:44 D. 1:54 E. 2:14 Follow a basic approach: \(Work=Rate*Time\)  \(Q\) is a rate of a qualified worker
 \(3\frac{Q}{4}\)  that of an apprentice
 \(\frac{Q}{5}\)  that of a trainee
When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+\frac{3}{2}Q+\frac{2}{5}Q)T\) \(5 = \frac{29}{10}T\) So, \(T=\frac{50}{29}\) or 1:44. Answer: C Hi Bunuel, Would it be wrong to say that Q = 1/5 since it takes 5 hours to do the job? Thanks



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Re: M0003 [#permalink]
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20 Mar 2015, 05:55
safaria25 wrote: Bunuel wrote: Official Solution:A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working \(\frac{3}{4}\) as fast and 2 trainees both working \(\frac{1}{5}\) as fast as he. If the fiveperson team digs the same well, how much time does the team need to finish the job? A. 1:24 B. 1:34 C. 1:44 D. 1:54 E. 2:14 Follow a basic approach: \(Work=Rate*Time\)  \(Q\) is a rate of a qualified worker
 \(3\frac{Q}{4}\)  that of an apprentice
 \(\frac{Q}{5}\)  that of a trainee
When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+\frac{3}{2}Q+\frac{2}{5}Q)T\) \(5 = \frac{29}{10}T\) So, \(T=\frac{50}{29}\) or 1:44. Answer: C Hi Bunuel, Would it be wrong to say that Q = 1/5 since it takes 5 hours to do the job? Thanks _______ Yes, that's correct.
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Re: M0003 [#permalink]
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19 Apr 2015, 02:40
What I did to convert 50/29 was to first get the mix number 1 21/29 => 1 hour and 21/29 minutes.
21/29 is approximately 21/30 ==> 21/29 is approximately 42/60.
Since I increased the denominator by 1 in my estimation, the real value should be bigger. 44 is closest to 42 therefore answer is 1 hour and 44 minutes



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Re: M0003 [#permalink]
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09 Jul 2015, 09:14
Bunuel wrote: Official Solution:A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working \(\frac{3}{4}\) as fast and 2 trainees both working \(\frac{1}{5}\) as fast as he. If the fiveperson team digs the same well, how much time does the team need to finish the job? A. 1:24 B. 1:34 C. 1:44 D. 1:54 E. 2:14 Follow a basic approach: \(Work=Rate*Time\)  \(Q\) is a rate of a qualified worker
 \(3\frac{Q}{4}\)  that of an apprentice
 \(\frac{Q}{5}\)  that of a trainee
When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+\frac{3}{2}Q+\frac{2}{5}Q)T\) \(5 = \frac{29}{10}T\) So, \(T=\frac{50}{29}\) or 1:44. Answer: C I thought "both capable of working 3/4 as fast..." means that 2 people together work 3/4 as fast as the qualified worker. I think adding to word "each" would be more easier to understand the question.



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Re: M0003 [#permalink]
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11 Jan 2016, 15:55
5 hours = 300 minutes = 1 Total job at the Qualified Rate.
Apprentices: 3/2 Q Trainees: 2/5 Q
(1/300)+(3/2)(1/300)+(2/5)(1/300)T= 1 Job in minutes
Eventually you get 3000/29 close to 3000/30 = 100 minutes but since I rounded the denominator up I have to round the minutes up.



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Re: M0003 [#permalink]
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20 Feb 2016, 13:26
Bunuel wrote: A qualified worker digs a well in 5 hours. He invites 2 apprentices, each working \(\frac{3}{4}\) as fast as the qualified worker and 2 trainees each working \(\frac{1}{5}\) as fast as the qualified worker. If the fiveperson team digs the same well, approximately how much time does the team need to finish the job?
A. 1 hour 24 minutes B. 1 hour 34 minutes C. 1 hour 44 minutes D. 1 hour 54 minutes E. 2 hours 14 minutes I had a slightly different approach. rate for worker  1/5 time apprentice finishes is 4/3 x5 = 20/3 hours. thus, the rate for 1 apprentice is 3/20. for 2 is 3/10. time of the traine is 5x5=25 hours. rate of 1 trainee 1/25. of 2 trainees = 2/25. ok, so in 1 hour, they will have: 1/5+3/10+2/25 or 29/50 finished. we thus know for sure that it requires less than 2 hours to finish the job. we are left with 21/50 of the job. we know the rate of all people  29/50 per hour. thus, the time remaining to finish the job will be: 21/50 x 50/29 = 21/29. multiply this by 60 minutes > suppose you have 21*60/30 = 21*2 = 42 mins. since denominator was increased, we can think that the mins should be around 42.. only C works.



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Re: M0003 [#permalink]
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11 Sep 2016, 06:53
Is there any other way to solve this question apart from what Bunuel has given?



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Re: M0003 [#permalink]
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11 Sep 2016, 09:09
Let the total work be 100 units.
Rate of the qualified worker  100/5  20 units/hr Rate of the apprentices  3/4 * 20  15 units/hr . Since 2 apprentices , it will be 30 units/hr Rate of the trainees  1/5 * 15  3 units/hr. Since 2 trainees, it will be 6 units/hr
So, the total work done by all of these 5 workers per hour is  56 units. But the total work is 100 units, so still 45 units of work needs to be done.
60 mins  56 units. 1 min  56/60 units  14/15 units 45 mins  42 units can be done.
So for approx 1hr 45mins 98 units of work can be done. I'd go with a nearest answer, which would be C.



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Re: M0003 [#permalink]
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11 Sep 2016, 09:23



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Rate of work from Qualified worker = 1/5
rate of work for a App= 1/5 *3/4=3/20 and for 2 App= 3/20*2= 3/10
rate of work for tra = 1/5*1/5 and for two of them= 2/25
total = 1/5+3/10+2/25 = 29/50
w=r.t 1=29/50 (t) t = 50/29



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Re: M0003 [#permalink]
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05 May 2017, 00:22
Bunuel wrote: Follow a basic approach: \(Work=Rate*Time\) \(Q\) is a rate of a qualified worker. \(\frac{3}{4}*Q\)  that of an apprentice. \(\frac{1}{5}*Q\)  that of a trainee. When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+2*(\frac{3}{4}*Q)+2*(\frac{1}{5}*Q))*T\). \(5 = \frac{29}{10}*T\). So, \(T=\frac{50}{29}\) or approximately 1 hour 44 minutes.
Answer: C Hi, I do not understand how W became equal to 5Q. Could you elaborate this part? \(W = 5Q=(Q+2*(\frac{3}{4}*Q)+2*(\frac{1}{5}*Q))*T\).
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Re: M0003 [#permalink]
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05 May 2017, 02:59
ashikaverma13 wrote: Bunuel wrote: Follow a basic approach: \(Work=Rate*Time\) \(Q\) is a rate of a qualified worker. \(\frac{3}{4}*Q\)  that of an apprentice. \(\frac{1}{5}*Q\)  that of a trainee. When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+2*(\frac{3}{4}*Q)+2*(\frac{1}{5}*Q))*T\). \(5 = \frac{29}{10}*T\). So, \(T=\frac{50}{29}\) or approximately 1 hour 44 minutes.
Answer: C Hi, I do not understand how W became equal to 5Q. Could you elaborate this part? \(W = 5Q=(Q+2*(\frac{3}{4}*Q)+2*(\frac{1}{5}*Q))*T\). We are given that a qualified worker digs a well in 5 hours, so if the rate of a qualified worker is Q, then from the formula work = time*rate, we'll get work = 5Q. Hope it's clear.
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Re: M0003 [#permalink]
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06 May 2017, 13:09
efficiency of qualified w=1/5 per hr efficiency of apprentices=1/5 * 3/4 = 3/20 per hr efficiency of trainee=1/5 * 1/5=1/25 per hr total work done in 1 hr 1/5 + 3/20*2 + 1/25 *2 = 29/50 full work will be done in 50/29= 1 hr 44 min ans: c



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Re: M0003 [#permalink]
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11 May 2017, 15:41
I'm glad I'm not the only one who saw the hard part as finding 50/29!
Long division takes too long. 50/29 is close to 50/30, which is 5/3. Remember that by making the denominator bigger, the true value of the fraction will be smaller. 5/3 is 1 and 2/3. 2/3 of one hour is 40 minutes. So the estimation is one hour and 40 minutes, with the true value being a little bigger.
B is 1 hour and 34 minutes C is 1 hour and 44 minutes
It's cutting it very close...but for the sake of time answer C is the better answer. I'm not sure of a quicker easier way than this



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Re M0003 [#permalink]
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08 Oct 2017, 08:20
Hi, If I solve the question by using method : 2 apprentices2*3/4*5=7.5 hours 2 trainees2*(1/5)*5=2 hours 1 worker5 hours
so,(1/7.5 +1/2+1/5) * x=1 so comes out to be 1 hr 12 min. Please help,where I am going wrong







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