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Intern  Joined: 04 Feb 2011
Posts: 43
Location: US
Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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Difficulty:   5% (low)

Question Stats: 83% (01:25) correct 17% (01:59) wrong based on 330 sessions

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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
Manager  Joined: 14 Feb 2011
Posts: 144
Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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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

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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Joined: 02 Sep 2009
Posts: 58450
Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

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3
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.

Must know to solve work problems: word-translations-rates-work-104208.html#p812628
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GPA: 3.75
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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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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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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$$= \frac{840}{7} = 120 Minutes = 2 Hours$$

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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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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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_________________ 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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