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Machine A working alone can complete a job in 3 1/2 hours. Machine B

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Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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New post 08 Mar 2011, 02:23
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Question Stats:

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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
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Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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New post 08 Mar 2011, 02:37
Lolaergasheva wrote:
Machine A working alone can complete a job in hours. Machine B working alone can do the same job in 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) 2 hr
(C) 4 hr 5 min
(D) 7 hr
(E) 8 hr 10 min

I got answer E but it is incorrect


I think the question is incomplete in its present form. The details of number of hours for both machines is not there. If they were given (say x and y), then you could get the total number of hours by simple formula of 1/x+1/y = 1/combined rate
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Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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New post 08 Mar 2011, 03:16
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Lolaergasheva wrote:
Machine A working alone can complete a job in hours. Machine B working alone can do the same job in 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) 2 hr
(C) 4 hr 5 min
(D) 7 hr
(E) 8 hr 10 min

I got answer E but it is incorrect


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
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Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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New post 26 Sep 2014, 12:57
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?

--just remember rate*time=job
Lets consider they both need to work for t hours to get the job done..

So, rate*time=job (Here job is 1 as it needs to be completed)
rate for type A machine =1/210 -- converting hrs to minutes
similarly rate for type A machine =1/280

Finally we have,
(1/210)*t + (1/280)*t=1
t=280*210/490
t=120 mins=2 hrs

Answer B should be correct.
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Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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New post 30 Sep 2014, 01:36
4
\(3 \frac{1}{2}\) 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
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Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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New post 01 Oct 2014, 00:14
The question is quit simple, we need not convert them to minutes.

Machine A : 3 1/2 hrs = 7/2 hrs. So, in one hour the work would be 2/7.

Machine A : 4 2/3 hrs = 14/3 hrs. So, in one hour the work would be 3/14.

Combined rate of both machines,

2/7 + 3/14 = 7/14 = 1/2.

So, the complete work is done in 2 hours.
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Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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New post 23 Jan 2019, 18:14
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Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B   [#permalink] 23 Jan 2019, 18:14
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