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Each of 10 machines works at the same constant rate doing a

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Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 12 Jun 2010, 10:50
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Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, to complete the job is 16 hours. How many hours would be needed if only 8 machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26

In the test I ticked the answer as 20, which was correct but it was random guess. Can someone explain how to solve these questions? What to equate? what to look for? etc.etc. i.e what is the main logic behind to solve these problems.
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 12 Jun 2010, 12:02
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gsaxena26 wrote:
Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, o complete the job is 16 hours. How many hours would be needed if only 8 machines, working together, were used to complete the job?

18
20
22
24
26

In the test I ticked the answer as 20, which was correct but it was random guess. Can someone explain how to solve these questions? What to equate? what to look for? etc.etc. i.e what is the main logic behind to solve these problems.


Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance.

Time*Rate=Distance
Time*Rate=Job

Given: \(16*10x=job\). Question: if \(t*8x=job\) (the same job), then \(t=?\)

Solving for \(t\): \(16*10x=t*8x\) --> \(t=20\).

Answer: B.

Hope it helps.
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 15 Jun 2010, 10:18
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go by this split:

10 Machines--16Hrs--1work
1 Machines--160Hrs--1work
8 Machines--20Hrs--1work
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 12 Jun 2010, 12:36
So correct me if I am wrong:

x -> Rate of 1 machine and therefore rate of 10 machines is 10x.

I understand the rest of it. Thanks.
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 12 Jun 2010, 12:46
gsaxena26 wrote:
So correct me if I am wrong:

x -> Rate of 1 machine and therefore rate of 10 machines is 10x.

I understand the rest of it. Thanks.


Yes, that is correct.

Below are some work problems with explanations:
ps-explanation-92679.html#p713495
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal

Hope it helps.
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 15 Jun 2010, 12:23
gsaxena26 wrote:
Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, o complete the job is 16 hours. How many hours would be needed if only 8 machines, working together, were used to complete the job?

18
20
22
24
26

In the test I ticked the answer as 20, which was correct but it was random guess. Can someone explain how to solve these questions? What to equate? what to look for? etc.etc. i.e what is the main logic behind to solve these problems.


1job/16hrs for 10 machines. Thus (1/16)/10 -> 1/160hrs for 1 machine. -> 1/160*8 = 1/20 -> 20 hrs.
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 16 Jun 2010, 02:33
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gsaxena26 wrote:
Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, o complete the job is 16 hours. How many hours would be needed if only 8 machines, working together, were used to complete the job?

18
20
22
24
26

In the test I ticked the answer as 20, which was correct but it was random guess. Can someone explain how to solve these questions? What to equate? what to look for? etc.etc. i.e what is the main logic behind to solve these problems.



I would do this question as under:

Let total work be 160 pages

At present
10 machines take 16 hours each to type 160 pages
That gives one machine types 16 pages in 16 hrs or 1 page per hour

Required
8 machines and 160 pages

Obviously given the speed of 1 page per hour the total time required would be 20hrs.

Hope this helps....
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 16 Jan 2011, 08:12
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i usually convert such questions into machine-hours

10 machines in 16 hours = \(10*16\) machine-hours

8 machines will take = \(\frac{10*16}{8} = 20\) hours

Answer: B

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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 26 Oct 2013, 12:44
gsaxena26 wrote:
Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, o complete the job is 16 hours. How many hours would be needed if only 8 machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26

In the test I ticked the answer as 20, which was correct but it was random guess. Can someone explain how to solve these questions? What to equate? what to look for? etc.etc. i.e what is the main logic behind to solve these problems.



This is a case of direct inverse variation

Number of Machine varies inversely with time
i.e as number of machines will increase ,time taken to complete job would become less .

10 Machine .........16 hrs
8 machine.......... x hrs?
x = 16 *(10/8)
x = 20 hrs
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 26 Oct 2013, 22:02
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The general formula is

MDH/w = constant i.e M1D1H1/W1 = M2D2H2/W2 where M = man/machines D = days H = hours in days and W = work

Here D & W are constant so M1H1 = M2H2 => 10*16 = 8* x => x= 20
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 10 Jan 2015, 23:22
1/16th of the work is completed in 1hr by 10 machines .
???? of the work is completed in 1 hr by 1 machine ----> 1/160th of the work is completed by 1 machine in 1 hr.

8 machines in 1 hr complete ---> 8 *1/160 = 1/20th of the work.
20 hrs needed for whole machines.
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 11 Feb 2015, 12:53
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gsaxena26 wrote:
Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, to complete the job is 16 hours. How many hours would be needed if only 8 machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26

In the test I ticked the answer as 20, which was correct but it was random guess. Can someone explain how to solve these questions? What to equate? what to look for? etc.etc. i.e what is the main logic behind to solve these problems.



Rate
10 Machine = 1/16
1 Machine = 1/160
8 Machine = 1/20

Rate x Time = Work
1/20 x T= 1
so T = 20
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 26 Sep 2016, 11:32
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gsaxena26 wrote:
Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, to complete the job is 16 hours. How many hours would be needed if only 8 machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26


The amount of the time needed by the 10 machines working together, to complete the job is 16 hours.
So, we can say that the job requires a total of 160 MACHINE HOURS (10 machines each working 16 hours = 160 machine hours)

How many hours would be needed if only 8 of the machines, working together, were used to complete the job?
We need to divide the work of 160 machine hours among the 8 machines.
160/8 = 20 hours

Answer:

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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 26 Sep 2016, 12:00
gsaxena26 wrote:
Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, to complete the job is 16 hours. How many hours would be needed if only 8 machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26


Let total work be 160 units

So, Efficiency of each machine is 1 unit...

Time required by 8 machines, working together will be 160/8 = 20 hours..

Hence answer will be (B) 20

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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 26 Jun 2017, 18:01

Since work done is the same, we can equate the two equations


Rate of 10 machines is 10*R, time is 16hrs
Rate of 8 machines is 8*R, time is t hrs

8R*t = 10R*16
t=20

Answer is B
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 20 Aug 2018, 09:31
rate of 10 machines \(= \frac{1}{16}\)
rate of 1 machine \(= \frac{1}{160}\)
rate of 8 machines \(= 8/160 = \frac{1}{20}\)
so 8 machines would require 20 hours to complete job.
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New post 20 Aug 2018, 10:57
20 hours. Check out the solution

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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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New post 01 Sep 2019, 01:39
Machines (M), Work (W) and Time (T)

M T W
10 16 1
1 16 1/10
1 1 1/160
8 1 1/20
8 20 1

Ans: 20 Hours
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Re: Each of 10 machines works at the same constant rate doing a   [#permalink] 09 Oct 2019, 01:58
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