Work Problem Calculator (People Needed)
If a job takes P people D days, find how many people are needed to finish it in d days. Shows the total work and step-by-step solution.
Input
Describe a job by a base number of people and days, then find how many people are needed to finish it within a target number of days.
Example: a job that takes 4 people 12 days, to be finished in 8 days. Enter positive numbers for people and days.
Result
People needed
6people
Total work
48 person-days
People needed per day
6 people
How to solve it
Find the total work. It is people times days, so 4 times 12 equals 48 person-days.
Divide the total work by the target days. 48 divided by 8 equals 6, which is the people needed.
It divides evenly, so the answer is 6 people.
Idea: by measuring work as people times days (person-days), the people needed is simply the total work divided by the target days.
How it works
- The total amount of work can be measured as people times days. If one person does one unit of work per day, a job done by P people in D days has a total of P times D units.
- Dividing the total work by the target number of days d gives the number of people needed per day, which is the people needed. The formula is people needed equals (P times D) divided by d.
- People cannot be split, so when the result is not a whole number it is rounded up. Rounding down would leave the job unfinished.
- All inputs are assumed to be positive numbers. Zero or negative values cannot be calculated.
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Work Problem Calculator (People Needed)