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# Working simultaneously and independently at an identical

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Senior Manager
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Working simultaneously and independently at an identical [#permalink]

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10 Dec 2010, 05:21
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Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8
[Reveal] Spoiler: OA

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Ajit

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Re: Rate problem [#permalink]

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10 Dec 2010, 05:37
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ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

The rate of 4 machines is rate=job/time=x/6 units per day --> the rate of 1 machine 1/6*(x/6)=x/24 units per day;

Now, again as {time}*{combined rate}={job done} then 4*(m*x/24)=3x --> m=18.

Or as 3 times more job should be done in 1.5 times less days than 3*1.5=4.5 times more machines will be needed 4*4.5=18.

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Re: Rate problem [#permalink]

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10 Dec 2010, 05:33
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ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

4 machines and 6 days so the total work done is 24

4x6=24
now 3 times the work is 72

So in 4 days if the work is to be completed its 72/4 = 18
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Re: Rate problem [#permalink]

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21 Sep 2012, 11:42
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ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

4 machines----------x units-----------6days
4 machines---------3x units-----------3*6 = 18 days
M machines---------3x unites----------4 days
The number of days and the number of machines which produce a certain number of units (in this case 3x) are inversely proportional.
This is because all the machines have the same constant rate.
Necessarily 4*18=M*4, therefore M = 18.

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Re: Working simultaneously and independently at an identical [#permalink]

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14 Sep 2015, 05:54
4
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ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8

solving in shortcut

m1 d1 h1 / w1 = m2 d2 h2/w2
4x6/x = mx4/3x

solving we get m=18

press kudos if you love my shortcut
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Re: Rate problem [#permalink]

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21 Sep 2012, 14:19
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This is a variation of the Distance = Rate * Time

Except we modify and say Output = # Machines * (Rate * Time)

X = # * r*t

X = 4 * r * 6
x = 24r
r = x/24

Solve for r because we want to find out the rate...then apply that rate to the new situation, which is output of 3x in 4 days

3x = N * r * 4

3x = N * (x/24) * 4
3x = N * (x/6)

18x = N *x
18 = N

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Re: Working simultaneously and independently at an identical [#permalink]

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09 Apr 2016, 14:05
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4 machines can do x work in 6 days
4 machines can do x/6 work in 1 day
1 machine can do x/6*1/4 work in 1 day

so,

n machines in 4 days= 3x work
n machines in 1 day = n * (x/6*1/4)
n machines in 4 days = n * (x/6*1/4)*4

Hence, n machines can do n*(x/6*1/4)*4 work in 4 days i.e. n*(x/6*1/4)*4 =3x ====>>>> n=18

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Re: Working simultaneously and independently at an identical [#permalink]

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30 Jan 2017, 03:45
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1) First let's set up an equation for the 4 machines and find a rate of each machine: $$4r*6=x; 4r=\frac{x}{6}, r=\frac{x}{6}*\frac{1}{4}, r=\frac{x}{24}$$
2) Now let's set up an equation for 3x units: let N be the number of machines, then $$N*\frac{x}{24}*4=3x; N*\frac{x}{6}=3x, N=\frac{3x}{x/6}=18$$

The correct answer is B.

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Re: Rate problem [#permalink]

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21 Sep 2012, 10:16
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Rate*Time = Work
(4R)*(6)=x ( Total 4 machines)
therefore R=x/24

now again (n)*(x/24)*(4) = 3x

solving for n, we get n=18 nos.

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Re: Working simultaneously and independently at an identical [#permalink]

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02 Feb 2017, 10:58
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ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8

We are given that 4 machines can complete x units in 6 days. Thus, the rate of the 4 machines is x/6.

Next we need to determine the number of machines needed to produce a rate of 3x/4. To calculate that number of machines, we can use the following proportion in which the value in each numerator is the number of machines and the value in each denominator is the corresponding rate of those machines. We can let n = the number of machines needed:

4/(x/6) = n/(3x/4)

24/x = 4n/3x

72x = 4nx

18 = n

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Re: Working simultaneously and independently at an identical [#permalink]

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05 Aug 2017, 13:34
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ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8

This is a wonderful problem to make an educated guess on. Rates & work problems are great for guessing in general.

Four machines make a certain amount of stuff in 6 days. We want to make three times as much stuff. That means we need at least three times as many machines, unless we also get extra time! (We don't.) So, eliminate 8.

We also have fewer days to spend making the stuff than we did originally. So, we can't get away with just having three times as many machines. We need more than three times as many. Eliminate 12.

Do we need 24 machines, though? That's 6 times as many as we had before. If you have six times as many machines, and you're only trying to make three times as much stuff, you should need half as much time. But we needed 4 days, not 3. Eliminate 24.

Guess 16 or 18 and move on!
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Re: Working simultaneously and independently at an identical [#permalink]

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14 Nov 2012, 05:50
$$\frac{4}{m}=\frac{x}{6}==>m=\frac{24}{x}$$

Calculate number of machines to produce 3x in 4 days:

$$N(\frac{x}{24})(4)=3x==> N=18$$
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Re: Working simultaneously and independently at an identical [#permalink]

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08 Jan 2017, 16:41
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Here's a way to solve this question quickly:

Here's a more in-depth look at a reliable approach for combined work questions with multiple identical machines:

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Re: Working simultaneously and independently at an identical [#permalink]

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21 Jul 2017, 04:00
mailnavin1 wrote:
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

4 machines and 6 days so the total work done is 24

4x6=24
now 3 times the work is 72

So in 4 days if the work is to be completed its 72/4 = 18

hi

you said total work done is 24 (4*6), without calculating any rate of any machine. is this because all machines have the same rates ...? please say to me ..

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Re: Working simultaneously and independently at an identical [#permalink]

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21 Jul 2017, 04:25
Bunuel wrote:
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

The rate of 4 machines is rate=job/time=x/6 units per day --> the rate of 1 machine 1/6*(x/6)=x/24 units per day;

Now, again as {time}*{combined rate}={job done} then 4*(m*x/24)=3x --> m=18.

Or as 3 times more job should be done in 1.5 times less days than 3*1.5=4.5 times more machines will be needed 4*4.5=18.

hi

"3 times more job should be done in 1.5 times less days than 3*1.5=4.5 times more machines will be needed 4*4.5=18."

i must say beautiful concept. please clarify the science underlying this concept ...

if this was such that 3 times more jobs be done within the same amount of time, 3 times more machines would be needed, provided all machines have the same rates..
if this was such that 3 times more jobs be done in 1.5 times more days, 1.5 times more machines would be needed, provided all machines have the same rates...

am I right ..?

thanks in advance ...

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Working simultaneously and independently at an identical [#permalink]

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05 Aug 2017, 08:21
Perhaps someone can chime in on my solution -

I've just took the LCM of 4 and 6 to be 12 thus X = 12.

4 Machines create a total product P of 12 in 6 days, working at a rate of 0.5 per machine per day.

We need 3x of product so 3(12) = 36 of product within 4 days.

So how many machines will it take to create 36 units of product at a rate of 0.5 per day within 4 days?

18.

Is this a valid solution? Was easier for me to conceptualize than other more sophisticated answers.

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Working simultaneously and independently at an identical [#permalink]

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18 Sep 2017, 03:11
Please correct me if I am wrong: I tried to make it simpler by step-by-step approach:
- 4M produces x units in 6 days
- 4M produces 3x units in (3) (6) = 18 days
- 4M produces 3x units in 18 days, so double the machines and half the number of days to 4 until you arrive at the number you want

We have about 16 machines producing 3x units in 4.5 days, clearly. Therefore, eliminate other options, and pick up something more than 16 days, i.e. 18 (answer choice 'B')
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Working simultaneously and independently at an identical   [#permalink] 18 Sep 2017, 03:11
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