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Working simultaneously and independently at an identical [#permalink]

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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?

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.

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

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14 Sep 2015, 06:54

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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

answer b

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Please press+ 1kudos if you appreciate this post and for motivation !!

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

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30 Jan 2017, 04:45

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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 \(N*\frac{x}{24}*4=3x; N*\frac{x}{6}=3x, N=\frac{3x}{x/6}=18\)

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.

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

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09 Sep 2015, 19:47

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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

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

Answer: B
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