Work-Rate Days Calculator
Find how many days it takes p workers to finish a job that P workers do in D days. Shows the total work and a step-by-step solution.
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Input
Enter the reference number of workers and days, plus the actual number of workers, to find how many days the job will take.
This finds the days needed when p workers do a job that takes P workers D days.
Result
Days needed
12days
Total work
48 worker-days
Daily progress
4 worker-days per day
How to solve it
Find the total work. With 6 workers for 8 days, the total work is 6 times 8 = 48 worker-days.
Find the daily progress. With 4 workers, the job advances by 4 worker-days each day.
Divide the total work by the daily progress: 48 divided by 4 = 12 days.
Idea: total work = workers times days. Days = total work divided by workers = (P times D) divided by p. Each worker is assumed to do the same amount per day.
How it works
- Treat the total work as the product of workers and days, measured in worker-days. With P workers for D days, the total work is W = P times D.
- With p workers actually on the job, the daily progress is proportional to the number of workers, so it equals p units per day.
- The required number of days is the total work divided by the daily progress: days = W divided by p = (P times D) divided by p.
- The model assumes each worker completes the same amount per day, and more workers add proportionally more progress each day.
- When the result is not a whole number, the calculator also shows the days rounded up, since finishing the job needs a whole number of working days.
Frequently asked questions
- How is the number of days calculated?
- The total work is treated as person-days, so W = P × D from the baseline of P workers over D days. With p workers actually on the job, the days needed are W ÷ p = (P × D) ÷ p.
- What assumptions does this rely on?
- It assumes each worker completes the same amount per day, so daily progress rises in proportion to the number of workers. Because of this, the work done per day is directly proportional to p.
- What happens when the days do not divide evenly?
- If the result has a fraction, the tool also shows the days rounded up to the next whole number needed to finish. Use that as a guide for how many days you actually have to allow.
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