Work and time calculator
Work out how long a job takes when several workers, machines or pipes work together. Enter how long each takes alone. Answers are exact fractions as well as decimals, and the working is shown.
Worked example
With the values shown above when the page opens:
Working together they take 4 (4)
- Each person's rate = 1 ÷ their time: 1/12 + 1/6
- Combined rate = 1/4 of the job per unit of time
- Time together = 1 ÷ 1/4 = 4 = 4
How it works
- Think in rates: someone who finishes a job in 12 hours does 1/12 of it per hour.
- When people work together their rates add up. Two people taking 12 and 6 hours do 1/12 + 1/6 = 1/4 of the job per hour, so together they take 4 hours.
- A pipe that empties the tank has a negative rate, so subtract it. If the fill rate is not larger than the drain rate, the tank never fills.
Questions
Why can I not just average the times?
Rates add, times do not. Two machines taking 12 and 6 hours do not take 9 hours together; they take 4.
Does it matter if the workers work at different speeds?
No. Each worker is described by their own time alone, so different speeds are already included.
What if one worker joins later?
Split the job into stages: work out how much is done before they join, then use the combined rate for the rest.
Related
Calculators are for learning and quick checks. Check important figures yourself, and do not rely on them for tax, legal or financial decisions.