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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
A. 10min
B. 12min
C. 15min
D. 18min
E. 20min
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27 Jul 2017, 19:05
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MathRevolution
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
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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28 Jul 2017, 08:56
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MathRevolution
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.A. 10min
B. 12min
C. 15min
D. 18min
E. 20min
\(r= W/t\)
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
