The fundamental relationship between work (W), rate (R), and time (T) is given by:
W=R×T
This formula can be rearranged to solve for rate or time:
- R=TW
- T=RW
When multiple workers are involved, their individual rates can be combined to find the total rate. If Worker A can complete a job in TA time and Worker B can complete the same job in TB time, their combined rate is:
Rcombined=TA1+TB1
The time taken to complete the job together is:
Tcombined=Rcombined1=TA+TBTA×TB
For example, if Worker A can complete a job in 6 hours and Worker B can complete it in 3 hours, their combined rate is:
Rcombined=61+31=21
Thus, the time taken to complete the job together is:
Tcombined=211=2 hours
In problems where work is done in parts or stages, calculate the work done at each stage and sum the results. For example, if a worker completes half the job in 2 hours, the remaining half can be completed at the same rate or a different rate, depending on the problem.
Some problems involve workers with varying rates. For example, a worker might work at one rate for a certain period and then switch to a different rate. In such cases, calculate the work done in each period separately and sum the results.
In problems involving rest periods, calculate the effective working time by subtracting the rest periods from the total time. For example, if a worker works for 2 hours and then rests for 1 hour, the effective working time over a 6-hour period is:
Effective Time=2×2=4 hours
