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505-555 (Easy)|   Work and Rate Problems|                              
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Hi math expert Bunuel,
Can you please let me know about any practice problems similar to this?
Would really appreciate your help!
Thanks
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Hi math expert Bunuel,
Can you please let me know about any practice problems similar to this?
Would really appreciate your help!
Thanks


17. Work/Rate Problems



On other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
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Bunuel
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

Kudos for a correct solution.

Let's assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6.

Let's say x = 24

GIVEN: 4 machines make x units in 6 days
This means 4 machines make 24 units in 6 days
So, 4 machines make 4 units in 1 day [if you divide the work time by 6, the output is also divided by 6]
So, 1 machine makes 1 unit in 1 day [if you divide the number of machines by 4, the output is also divided by 4]

From here, we can answer the question 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?
If x = 24, 3x = 72
Our goal is to make 72 units in 4 days.

So, 1 machine makes 4 units in 4 days [if you multiply the work time by 4, the output is also multiplied by 4]
So, 18 machines make 72 units in 4 days [if you multiply the number of machines by 18, the output is also multiplied by 18]

Answer: B

Cheers,
Brent
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Video solution from Quant Reasoning:
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Bunuel
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

Answer: Option B

Video solution by GMATinsight

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4 machines - 6 days - x units
4 machines -18 days - 3x units
MM machines - 4 days - 3x units
then (4 machines)*(18 days)=(M machines)*(4 days) --> M = 18
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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4M*6 = X

Therefore: 3X = 4M*6*3

Now 3X work is 4M*6*3, therefore 4M*6*3/m*4 = 18 (in denominator 4 stands for days)
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Bunuel
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

Wanna make solving the Official Questions interesting???


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Answer: Option B

Video solution by GMATinsight


Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
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Thanks GMATinsight for the brilliant work rate machine formula here that make it easy peasy like a lemon squeezy :D :thumbsup: :please:
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Bunuel
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

I solved it in the unitary method.
6 days are required for 4 machines (to produce x units)
1 day is required for 4*6= 24 machines (to produce x units)
4 days are required for 24/4= 6 machines (to produce x units)

Now for 3x units, 3*6 =18 machines are required.
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Each machine has a rate of x/6 divided by 4 = x/24

To complete 3x work in 4 days you need a rate of

R T W
(3x/4 days) 4days 3X

Therefore number of machines needed is

Rate to complete in 4 days / individual machine rate

3x/4 / x/24 = 18 days
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Let's say one machine can produce r units of product P per day. Then, in 6 days, four machines can produce a total of 4r x 6 = 24r units of product P. We are given that this equals x, so:

24r = x

We want to know how many machines are needed to produce 3x units of product P in 4 days. Let's call the number of machines we need n. Then, in 4 days, n machines can produce:

nr x 4

units of product P. We want this to be equal to 3x, so:

nr x 4 = 3x

We can substitute x = 24r into this equation to get:

nr x 4 = 3 x 24r

Simplifying:

4nr = 72r

Dividing both sides by r (since r is not equal to 0):

4n = 72

So:

n = 18

Therefore, we need 18 machines to produce a total of 3x units of product P in 4 days. The answer is (B) 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?

4 machine ---- x units ---- 6 days

4 machine ---- 3x units --- 18 days

1 machine ---- 3x units ---- 72 days

N machine ---- 3x units ---- 4 days


=> 74/4 = 18 machines

Hope it helps! :)
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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
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