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08 Mar 2011, 02:23
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
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Question Stats:
85% (01:23) correct
15%
(02:03)
wrong
based on 1335
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Machine A working alone can complete a job in \(3 \frac{1}{2}\) hours. Machine B working alone can do the same job in \(4 \frac{2}{3}\) hours. How long will it take both machines working together at their respective constant rates to complete the job?
A. 1 hr 10 min
B. 2hr
C. 4hr 5 min
D. 7hr
E. 8 hr 10 min
A. 1 hr 10 min
B. 2hr
C. 4hr 5 min
D. 7hr
E. 8 hr 10 min
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08 Mar 2011, 03:16
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Lolaergasheva
PLEASE CHECK THE QUESTIONS WHEN POSTING.
Original question:
Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their respective constant rates to complete the job?
A. 1 hr 10 min
B. 2hr
C. 4hr 5 min
D. 7hr
E. 8 hr 10 min
General formula for multiple entities is \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously.
For example if:
Time needed for A to complete the job is A hours;
Time needed for B to complete the job is B hours;
Time needed for C to complete the job is C hours;
...
Time needed for N to complete the job is N hours;
Then: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}\), where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously.
For two and three entities (workers, pumps, ...):
General formula for calculating the time needed for two entities A and B working simultaneously to complete one job:
Given that \(t_1\) and \(t_2\) are the respective individual times needed for \(A\) and \(B\) (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\)).
For our original questions it'll be: 1/(7/2)+1/(14/3)=1/T --> T=2.
Answer: B.
Must know to solve work problems: word-translations-rates-work-104208.html#p812628
30 Sep 2014, 01:36
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\(3 \frac{1}{2}\) Hours \(= 3*60 + \frac{1}{2} * 60 = 210\)Minutes
\(4 \frac{2}{3} Hours = 4*60 + \frac{2}{3} * 60 = 280\) Minutes
Combined rate of both machines
\(= \frac{1}{210} + \frac{1}{280} = \frac{7}{840}\)
Time required\(= \frac{840}{7} = 120 Minutes = 2 Hours\)
Answer = B
\(4 \frac{2}{3} Hours = 4*60 + \frac{2}{3} * 60 = 280\) Minutes
Combined rate of both machines
\(= \frac{1}{210} + \frac{1}{280} = \frac{7}{840}\)
Time required\(= \frac{840}{7} = 120 Minutes = 2 Hours\)
Answer = B
