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Intern  Joined: 15 Nov 2009
Posts: 34
Each of 10 machines works at the same constant rate doing a  [#permalink]

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Question Stats: 90% (01:21) correct 10% (02:25) wrong based on 596 sessions

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58464
Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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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 $$t=?$$

Solving for $$t$$: $$16*10x=t*8x$$ --> $$t=20$$.

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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7
3
go by this split:

10 Machines--16Hrs--1work
1 Machines--160Hrs--1work
8 Machines--20Hrs--1work
General Discussion
Intern  Joined: 15 Nov 2009
Posts: 34
Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58464
Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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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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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.
Manager  Joined: 18 Feb 2010
Posts: 129
Schools: ISB
Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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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.

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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Senior Manager  B
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1
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

HTH
Intern  Joined: 01 Jan 2013
Posts: 48
Location: India
Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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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?

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
Intern  Joined: 29 Jan 2013
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Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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1
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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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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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?

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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Joined: 12 Sep 2015
Posts: 4019
Re: Each of 10 machines works at the same constant rate doing a  [#permalink]

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

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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

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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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

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

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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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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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