Combined rate shortcut? Not referring to A*B/A+B

Question

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

Bunuel · Answer

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.

Combined rate shortcut? Not referring to A*B/A+B

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