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.

Input

Enter the reference number of workers and days, plus the actual number of workers, to find how many days the job will take.

Reference workers P

workers

Reference days D

days

Actual workers p

workers

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.

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