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If 50 apprentices can finish a job in 4 hours and 30 skilled workers

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If 50 apprentices can finish a job in 4 hours and 30 skilled workers [#permalink]

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If 50 apprentices can finish a job in 4 hours and 30 skilled workers can finish the same job in 9/2 hours, how much of the job should be completed by 10 apprentices and 15 skilled workers in 1 hour?

(A) 1/9
(B) 29/180
(C) 26/143
(D) 1/5
(E) 39/121
[Reveal] Spoiler: OA

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Re: If 50 apprentices can finish a job in 4 hours and 30 skilled workers [#permalink]

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New post 16 Oct 2017, 11:11
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Bunuel wrote:
If 50 apprentices can finish a job in 4 hours and 30 skilled workers can finish the same job in 9/2 hours, how much of the job should be completed by 10 apprentices and 15 skilled workers in 1 hour?

(A) 1/9
(B) 29/180
(C) 26/143
(D) 1/5
(E) 39/121



hi..

If 50 apprentices can finish a job in 4 hours, 10 apprentices will finish it in \(4*\frac{50}{10}=20\)
so 1 hour work of 10 apprentices = \(\frac{1}{20}\)

and 30 skilled workers can finish the same job in 9/2 hours, so 15 will do it in 9 h
so 1 hour work of 15 skilled workers = \(\frac{1}{9}\)

so their combined work = \(\frac{1}{20}+\frac{1}{9}=\frac{29}{180}\)

B
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If 50 apprentices can finish a job in 4 hours and 30 skilled workers [#permalink]

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New post 16 Oct 2017, 11:55
If 50 apprentices can finish the job in 4 hours and
30 skilled workers can do the same work in 4.5 hours

We could assume the work to be 5400 units.
Hence each apprentice does 27 units of work/hour
Similarly, each skilled worker does 40 units of work/hour

So, 10 apprentices and 15 skilled workers will do 10*27 + 15*40 = 270+600 = 870

Therefore, they would have completed \(\frac{870}{5400} = \frac{29}{180}\)(Option B)
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If 50 apprentices can finish a job in 4 hours and 30 skilled workers [#permalink]

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New post 16 Oct 2017, 12:27
Bunuel wrote:
If 50 apprentices can finish a job in 4 hours and 30 skilled workers can finish the same job in 9/2 hours, how much of the job should be completed by 10 apprentices and 15 skilled workers in 1 hour?

(A) 1/9
(B) 29/180
(C) 26/143
(D) 1/5
(E) 39/121

Another way. Looks long. It isn't. Under 1:30

Find the rate of an individual apprentice and an individual skilled worker. Use that rate to figure out how much work gets finished when the number of workers change. (Just add # to the left side of the RT=W equation.)

Let # = number of workers

# * r * t = W

Individual rate of apprentice:
# = 50, r = ?? t = 4, W = 1

\(50 * r * 4 = 1\)
\(r_{a} = \frac{1}{(50*4)} = \frac{1}{200}\)

Individual rate of skilled worker:
# = 30, r = ??, t = 9/2, W = 1

\(30 * r *\frac{9}{2}= 1\)

\(r = \frac{1}{(30 * \frac{9}{2})}\)

\(r_{s} =\frac{1}{135}\)

Ten apprentices and 15 skilled workers, at their individual rates, work at respective collective rates.

10 apprentices' collective rate:
\((10 *\frac{1}{200}) =\frac{10}{200}=\frac{1}{20}\)

15 skilled workers' collective rate:
\((15 *
\frac{1}{135}) =\frac{15}{135}=\frac{1}{9}\)


Combined hourly rate of As and Ss:
\(\frac{1}{20} + \frac{1}{9} =\frac{29}{180}\)

Amount of work finished in one hour by all: \(\frac{29}{180} *
1 = \frac{29}{180}\)

Answer B

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Re: If 50 apprentices can finish a job in 4 hours and 30 skilled workers [#permalink]

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New post 19 Oct 2017, 16:58
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First, find individual rates.

Apprentices:

50 complete 1 job in 4 hours.
50 complete 1/4th of a job in 1 hour.
1 completes\(\frac{1}{4*50}\) or\(\frac{1}{200}\) of a job in 1 hour.

Similarly for skilled workers:

30 complete 1 job in 9/2 hours.
30 complete 2/9 of the job in 1 hour.
1 completes \(\frac{2}{9*30}\) or \(\frac{2}{270}\) or \(\frac{1}{135}\) job in 1 hour.

Work done by 10 Apprentices and 15 skilled workers in 1 hour = \(10*\frac{1}{200}+15*\frac{1}{135} = \frac{29}{180}\)
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If 50 apprentices can finish a job in 4 hours and 30 skilled workers [#permalink]

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New post 23 Oct 2017, 07:00
I got B. This would be a classic problem where I'd make a silly mistake, but it appears I might have avoided that.

If 50 apprentices can finish a job in 4 hours and 30 skilled workers can finish the same job in 9/2 hours, how much of the job should be completed by 10 apprentices and 15 skilled workers in 1 hour?

I knew I needed to find the individual rates of one worker per hour. If it takes a 50 workers 4 hours, that collectively means it takes the apprentices 200 total hours to compete the job. So the rate of one apprentice is 1/200.

I repeated this step for the skilled workers. It takes them collectively 135 hours to complete this job (30*4.5). So the skilled worker rate is 1/135.

10 * (1/200) + 15 *(1/135)= 10/200 + 15/135 which simplifies to 1/20+1/9, I expanded that to 9/180+20/180=29/189.
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Also, I appreciate any kudos.

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Re: If 50 apprentices can finish a job in 4 hours and 30 skilled workers [#permalink]

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New post 24 Oct 2017, 05:45
Bunuel wrote:
If 50 apprentices can finish a job in 4 hours and 30 skilled workers can finish the same job in 9/2 hours, how much of the job should be completed by 10 apprentices and 15 skilled workers in 1 hour?

(A) 1/9
(B) 29/180
(C) 26/143
(D) 1/5
(E) 39/121


The rate of 50 apprentices is 1/4 and the rate of 30 skilled workers is 1/(9/2) = 2/9.

We can use a proportion to determine n, the rate of 10 apprentices:

50/(1/4) = 10/n

200 = 10/n

200n = 10

n = 10/200 = 1/20

We can also use a proportion to determine m, the rate of 15 skilled workers:

30/(2/9) = 15/m

(9 x 30)/2 = 15/m

135 = 15/m

135m = 15

m = 15/135 = 1/9

Thus, the fraction of a job completed by 10 apprentices and 15 skilled workers in 1 hour is 1/20 + 1/9 = 9/180 + 20/180 = 29/180.

Answer: B
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Re: If 50 apprentices can finish a job in 4 hours and 30 skilled workers   [#permalink] 24 Oct 2017, 05:45
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