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Three machines operating independently, simultaneously, and
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09 Oct 2013, 19:23
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25% (medium)
Question Stats:
73% (01:33) correct 27% (01:44) wrong based on 733 sessions
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Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
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12 Feb 2015, 12:55
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Hi All,
These type of "work" questions can be solved in a variety of ways (depending on how you want to do the math).
Since we have 3 machines, each of which works for 36 hours to complete a job, we know that....
(3 machines)(36 hours each) = 108 machine-hours are needed to complete the job.
Since we're told that all the machines work at the same rate, adding a 4th machine is not going to be difficult to deal with. The 108 machine-hours are still needed to complete the job, but now we have 4 machines doing work instead of 3...
(108 machine-hours)/(4 machines) = 27 hours.
Since the original time was 36 hours and the "new" time is 27 hours, the difference is 9 hours.
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10 Oct 2013, 04:39
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Hi,
all 3 machine works at same rate = 1/x
1/x + 1/x + 1/x = 1/36 3/x = 1/36 x = 108.
Fourth machine was used with same rate (1/x) Total Rate for 4 MAchines = 4/x =4/108 =1/27 is the over all rate of four machine So time is 1/Rate = 27 hrs
Question asked was "how many fewer hours of simultaneous operation could the production order be fulfilled" so 36 - 27 = 9 Hrs
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17 Jul 2016, 12:48
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kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
A. 6 B. 9 C. 12 D. 27 E. 48
\(\frac{36}{3}=\) 12 hours (each machine take 12 hours) (3 machines * 12 hours) = (4 machines take x hours) 12 * 3 = 4 * X 36 = 4x 9 = x 4 machines will take 9 hours less to finish the same order Answer B
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22 Jul 2017, 19:03
kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
A. 6 B. 9 C. 12 D. 27 E. 48
Let C = the rate of one of the machines
3C = 1/36 C = 1/(36*3)
Add one more machine to determine the net impact...
4C = 4/(36*3) = 1/(9+3)
It would take 4 machines 27 hours to finish the job.
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07 Aug 2017, 09:27
Use inverse proportion concept to solve it quickly.
Initial number of machines=3 New Number of machines=4(after adding one more machine)
So number of machines increases by 1/3 of the initial number
Since time taken will be inversely proportional to the number of machines, therefore if number of machines increases by 1/3, time taken decrease by 1/4
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17 Oct 2018, 11:56
Attachment:
Screen Shot 2018-10-18 at 12.23.32 AM.png [ 38.2 KiB | Viewed 7843 times ]
If time taken by 4 machines is 27 hrs Time taken by 3 machines is 36 hrs. Question asks: how many fewer hours of simultaneous operation could the production order be fulfilled? 36-27 = 9 hrs Same work would take 9 fewer hours.
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Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled?
6 9 12 27 48
Total machine hours= 3 * 36 = 108 Now, no. of machines = 4 Total work hours will be same Therefore, work can be completed in hours = total hours/ no. of machines = 108/4 = 27 hours
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled?
6 9 12 27 48
Total no. of working hours of all the 3 machines = 3 * 36 = 108 hours
We add one more machine, but work will remain the same,
So new working hours completed by each machine = 108/4 = 27 hours
We want to know the difference between hours used in first and the second attempt,
Therefore, 36 - 27 = 9 (B)
Alternatively,
3 * 36 = Work ---- (I)
4 * X = Work ------(II)
Where X is no. of working hours when one machine is added.
Three machines operating independently, simultaneously, and
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25 Nov 2018, 09:00
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kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
A. 6 B. 9 C. 12 D. 27 E. 48
since the amount of work completed is the same, weather it will be 4 or 6 machines, I made following equation
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25 Nov 2018, 13:01
kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
Three machines operating independently, simultaneously, and
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02 Jan 2019, 11:43
Lets assume we have 36 units of work to be completed by 3 machines.
Therefore, we have 36 units = Rate x 36 hours =====> Rate = 1 unit/hour
Since prompt said the rate is constant for each machine, rate for one machine will be 1/3 unit/hour
Therefore, rate for 4 machines = 4 x 1/3 = 4/3 units per/hour
The time it will take for the 4 machines to complete 36 units of work = 36 units x 3/4 hours/unit = 9 x 3 = 27 hours
Finally, the fewer hours it takes for 4 machines = 36 - 27 = 9 hours (Answer choice B)
kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
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10 Apr 2019, 08:14
kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
A. 6 B. 9 C. 12 D. 27 E. 48
3 machines can do a work in 36 hours. 1 machine can do a work in 36*3 = 108 hours. 4 machines can do a work in 108/4 = 27 hours.
So number of fewer hours taken when 4 machines works simultaneously = 36 - 27 = 9 hours.
Answer B _________________
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