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There is a total of 1,800 pages that needs to be typed. If it takes 90

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Math Revolution GMAT Instructor
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There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink]

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27 Jul 2017, 17:58
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There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together?

A. 10min
B. 12min
C. 15min
D. 18min
E. 20min
[Reveal] Spoiler: OA

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There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink]

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27 Jul 2017, 19:05
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MathRevolution wrote:
There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together?

A. 10min
B. 12min
C. 15min
D. 18min
E. 20min

It takes $$90$$ minutes when "$$a$$" types alone to complete the work.

Rate of work of "$$a$$" $$= \frac{1}{90}$$

It takes $$45$$ minutes when "$$b$$" types alone to complete the work.

Rate of work of "$$b$$" $$= \frac{1}{45}$$

It takes $$30$$ minutes when "$$c$$" types alone to complete the work.

Rate of work of "$$c$$" $$= \frac{1}{30}$$

Rate of work of "$$a$$$$,$$$$b$$ and $$c$$" combined is;

$$\frac{1}{90} + \frac{1}{45} + \frac{1}{30}$$ $$=>$$ $$\frac{1 + 2 + 3}{90} = \frac{6}{90} = \frac{1}{15}$$

Therefore time taken to complete the job when $$3$$ of them work together $$= \frac{1}{(1/15)} = 15$$ mins.

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There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink]

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28 Jul 2017, 08:56
MathRevolution wrote:
There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together?

A. 10min
B. 12min
C. 15min
D. 18min
E. 20min

Another way: calculate rates using 1800 as $$Work$$, then divide by time $$t$$ = number of minutes it takes each person to complete all 1800 pages.

$$r= W/t$$

a = 1800 p/90 mins is $$(\frac{20p}{1 min})$$

b = 1800 p/45 min is $$(\frac{40p}{1 min})$$

c = 1800 p/30 min is $$(\frac{60p}{1 min})$$

In one minute, the three together can type 20 + 40 + 60 = 120 pages, i.e., $$(\frac{120p}{1 min})$$

1800 pages/120 pages in 1 minute = 15 minutes to finish when working together

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Re: There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink]

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28 Jul 2017, 11:16
Total To be typed divided by individual capacity of each.
A can type 1800/90 i.e 20 per minute . Similarly B can type 1800/45 and C can type 1800/30 per minute.
Therefore together they take 1800/(20+40+60)= 1800/120 = 15.

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Re: There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink]

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30 Jul 2017, 18:58
==> For work rate questions, if there is a “together and alone”, you need to solve the question reciprocally. In other words, A: 1,800pg/90mins, B:1,800pg/45mins, C: 1,800pg/30mins, and if you assume A&B&C:1,800pg/t mins, you get (1/90)+(1/45)+(1/30)=(1/t), and from (1+2+3)/90=1/t, you get t=15.

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Re: There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink]

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01 Aug 2017, 17:22
MathRevolution wrote:
There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together?

A. 10min
B. 12min
C. 15min
D. 18min
E. 20min

The combined rate of typists a, b, and c is:

1800/90 + 1800/45 + 1800/30 = 20 + 40 + 60 = 120 pages per minute.

Thus, when working together, the typists complete the job in 1800/120 = 15 minutes.

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Re: There is a total of 1,800 pages that needs to be typed. If it takes 90   [#permalink] 01 Aug 2017, 17:22
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