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# It takes 3 employees, who all work at the same rate, 5 hours to comple

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It takes 3 employees, who all work at the same rate, 5 hours to comple  [#permalink]

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11 Apr 2017, 22:58
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15% (low)

Question Stats:

87% (01:22) correct 13% (01:32) wrong based on 103 sessions

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It takes 3 employees, who all work at the same rate, 5 hours to complete the typing of a 500 page document. How long would it take 6 similar employees to complete a document with 750 pages?

A. 1.25
B. 2.5
C. 3.75
D. 5.5
E. 7.5

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Re: It takes 3 employees, who all work at the same rate, 5 hours to comple  [#permalink]

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11 Apr 2017, 23:44
1
Given that, 3 employees in 5hrs type 500 pages.
So, in 1 hr they will type 500/5 = 100 pages.

Now if 3 employees in 1hr type 100 pages.
then 6 employees in 1hr will type (100x6)/3 = 200 pages.

200 pages are printed in 1hr, then 750 pages will get printed in 750/200 = 3.75hrs.

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Re: It takes 3 employees, who all work at the same rate, 5 hours to comple  [#permalink]

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12 Apr 2017, 05:39
1
Top Contributor
Bunuel wrote:
It takes 3 employees, who all work at the same rate, 5 hours to complete the typing of a 500 page document. How long would it take 6 similar employees to complete a document with 750 pages?

A. 1.25
B. 2.5
C. 3.75
D. 5.5
E. 7.5

We can solve this question by using some logic.

It takes 3 employees, who all work at the same rate, 5 hours to complete the typing of a 500 page document
So, a 3-person team takes 5 hours to type 500 pages.
What if we increase the job by 50% and make it 750 pages?
Well, it will take 50% longer to complete that job.
That is, a 3-person team will take 7.5 hours to type 750 pages.
What happens if we double the size of the team and make it a 6-person team?
Well, doubling the size of the team, will cut the work time in HALF.
That is, a 6-person team will take 3.75 hours to type 750 pages.

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Brent
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Re: It takes 3 employees, who all work at the same rate, 5 hours to comple  [#permalink]

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19 Apr 2017, 15:54
Bunuel wrote:
It takes 3 employees, who all work at the same rate, 5 hours to complete the typing of a 500 page document. How long would it take 6 similar employees to complete a document with 750 pages?

A. 1.25
B. 2.5
C. 3.75
D. 5.5
E. 7.5

We are given that 3 employees, who all work at the same rate, can type 500 pages in 5 hours.

So, the rate of the 3 employees is 500/5 = 100 pages per hour. Let’s use a proportion to determine x, the rate of the 6 employees.

3/100 = 6/x

3x = 600

x = 200

Since time = work/rate, it takes 6 workers 750/200 = 3.75 hours to complete 750 pages.

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Re: It takes 3 employees, who all work at the same rate, 5 hours to comple  [#permalink]

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19 Apr 2017, 19:23
3 employees => 5 hrs => 500 pages
6 employees => 2.5 hrs => 500 pages
6 employees => ? hrs => 750 pages

work = rate x time
500 = r x 2.5
r = 200

work = rate x time
750 = 200 x t
t = 3.75

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Re: It takes 3 employees, who all work at the same rate, 5 hours to comple  [#permalink]

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20 Nov 2017, 17:30
1
Hi All,

We're told that it takes 3 employees, who all work at the same rate, 5 hours to complete the typing of a 500 page document. We're asked how long it would take 6 similar employees to complete a document that is 750 pages. The answer choices are 'spread out enough' that you can actually answer this question without doing too much math - you just need a little logic and a couple of 'comparisons.'

IF.... we were just doubling the number of employees, then the original job would take HALF of the time (2.5 hours instead of the original 5 hours). We're not doing the original job though - we're doing MORE work - so the time needed has to be GREATER than 2.5 hours.

Since we're doubling the number of employees, but we're NOT doubling the number of pages (that number is only increased by 50%), we know that the total amount of time would have to be LESS than 5 hours.

There's only one answer that falls in that range....

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It takes 3 employees, who all work at the same rate, 5 hours to comple  [#permalink]

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21 Nov 2017, 09:38
Bunuel wrote:
It takes 3 employees, who all work at the same rate, 5 hours to complete the typing of a 500 page document. How long would it take 6 similar employees to complete a document with 750 pages?

A. 1.25
B. 2.5
C. 3.75
D. 5.5
E. 7.5

(# of workers) * (rate) * (time) = Work

(Simply add one extra column, number of workers, to standard RTW table. Manipulate it the same way as RT = W.)

Individual worker rate, r?

(# of workers) * (rate) * (time) = Work$$^{1}$$

(3) * (r?) * (5) = 500

r = $$\frac{500}{(3*5)}=\frac{500}{15}=\frac{100}{3}$$

Use that rate to find time in the second scenario: At that rate, how much time will it take 6 workers to type 750 pages?

(# of workers) * (rate) * (time) = Work$$^{2}$$

6 * $$(\frac{100}{3}$$) * (t?) = 750

t = $$\frac{750}{(\frac{600}{3})}=\frac{750}{200}=\frac{15}{4}=3.75 hrs$$

What follows is just manipulation of equation

$$^{1} r =\frac{W}{(No.Workers*t)}$$

$$^{2}t = \frac{W}{(No.Workers * r)}$$

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It takes 3 employees, who all work at the same rate, 5 hours to comple &nbs [#permalink] 21 Nov 2017, 09:38
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