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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

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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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.

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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PhD in Applied Mathematics Love GMAT Quant questions and running.

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

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

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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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