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10 Jul 2014, 16:33
Kudos
Bookmarks
Hi,
Does anyone have a shortcut similar to the combined time shortcut in order to reach combined rates say when Machine A completes 20 widgets in 6 hours and Machine B completes 20 widgets in 8 hours? 20/6 + 20/8 (to get the combined rate) is very cumbersome and increases my risk of error in a game day environment.
Gratefully,
KC
Does anyone have a shortcut similar to the combined time shortcut in order to reach combined rates say when Machine A completes 20 widgets in 6 hours and Machine B completes 20 widgets in 8 hours? 20/6 + 20/8 (to get the combined rate) is very cumbersome and increases my risk of error in a game day environment.
Gratefully,
KC
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11 Jul 2014, 11:58
Kudos
Bookmarks
kacolema
For multiple entities: \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously.
For example if:
Time needed for A to complete the job is A hours;
Time needed for B to complete the job is B hours;
Time needed for C to complete the job is C hours;
...
Time needed for N to complete the job is N hours;
Then: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}\), where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously.
For two and three entities (workers, pumps, ...):
General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:
Given that \(t_1\) and \(t_2\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\)).
General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:
\(T_{(A&B&C)}=\frac{t_1*t_2*t_3}{t_1*t_2+t_1*t_3+t_2*t_3}\) hours.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
