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

Answer (C)...

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There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink] New post   28 Jul 2017, 08:56
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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

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

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

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Re: There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink] New post   30 Jul 2017, 18:58
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==> 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.

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


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.

Answer: C
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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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