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

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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12 Jun 2010, 12:02

8

17

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 \(t=?\)

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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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16 Jun 2010, 02:33

1

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.

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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?

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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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.

Re: Each of 10 machines works at the same constant rate doing a
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11 Feb 2015, 12:53

1

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?

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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26 Sep 2016, 11:32

Top Contributor

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

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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 _________________

Thanks and Regards

Abhishek....

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