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# M00-03

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Math Expert
Joined: 02 Sep 2009
Posts: 47101

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16 Sep 2014, 00:14
2
5
00:00

Difficulty:

95% (hard)

Question Stats:

56% (01:45) correct 44% (02:24) wrong based on 102 sessions

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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 five-person 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

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Posts: 47101

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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 five-person 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.

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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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Joined: 16 Nov 2014
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11 Jan 2015, 19:11
1
1
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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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 five-person 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.

Intern
Joined: 21 May 2013
Posts: 8

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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 five-person 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.

Hi Bunuel,

Would it be wrong to say that Q = 1/5 since it takes 5 hours to do the job?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 47101

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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 five-person 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.

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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19 Apr 2015, 02:40
1
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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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 five-person 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.

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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Joined: 05 Jul 2015
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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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20 Feb 2016, 13:26
1
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 five-person 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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11 Sep 2016, 06:53
Is there any other way to solve this question apart from what Bunuel has given?
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11 Sep 2016, 09:09
1
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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11 Sep 2016, 09:23
Thanks Argo
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11 Sep 2016, 11:39
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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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.

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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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.

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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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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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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08 Oct 2017, 08:20
Hi,
If I solve the question by using method :
2 apprentices-2*3/4*5=7.5 hours
2 trainees-2*(1/5)*5=2 hours
1 worker-5 hours

so,(1/7.5 +1/2+1/5) * x=1
so comes out to be 1 hr 12 min.
Re M00-03   [#permalink] 08 Oct 2017, 08:20

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