Group Work Rate Calculator
Calculate how long two people working together take.
About the Group Work
The classic work-rate problem: if one person can paint a room in 6 hours and another takes 3, how long does it take them together? The trap is that times do not add — rates do. This calculator handles any number of workers, each at their own pace, and returns the combined time.
How to use it
- Enter how long the first person takes working alone.
- Enter how long the second person takes alone.
- Add as many workers as you need, in the same units.
- Read the combined time. Everything must use the same unit — all hours or all minutes.
The formula
Convert each time into a rate — the fraction of the job done per hour — add the rates, then invert the total.
1/T = 1/t₁ + 1/t₂ + … + 1/tₙ
So for two workers this simplifies to the product over the sum: T = (t₁ × t₂) ÷ (t₁ + t₂). A worker who takes 6 hours completes 1/6 of the job per hour. Someone taking 3 hours does 1/3 per hour. Together they finish 1/6 + 1/3 = 1/2 per hour, so the whole job takes 2 hours.
Worked examples
| Worker A alone | Worker B alone | Combined rate | Together |
|---|---|---|---|
| 6 hours | 3 hours | 1/2 per hour | 2 hours |
| 4 hours | 4 hours | 1/2 per hour | 2 hours |
| 5 hours | 20 hours | 1/4 per hour | 4 hours |
| 2 hours | 3 hours | 5/6 per hour | 1 hour 12 min |
The third row is the one worth studying. Adding someone four times slower than you only cuts the job from 5 hours to 4 — a 20% saving. Slow help helps less than people expect.
Common mistakes
- Averaging the times. The most common error by far. Six hours and three hours does not give four and a half. Averaging gives a number longer than the fastest worker, which cannot be right.
- Mixing units. One time in hours and another in minutes will produce nonsense. Convert everything first.
- Adding the times together. Nine hours would be how long it takes if they took turns rather than working simultaneously.
- Using it for work that cannot be split. Two people cannot write one letter twice as fast. This assumes the job divides cleanly and both can work at once.
Terms explained
- Work rate
- The fraction of the whole job finished per unit of time. Someone who takes 8 hours works at 1/8 of the job per hour.
- Combined rate
- The sum of the individual rates. This is the quantity that adds — times never do.
- Reciprocal
- One divided by a number. Time and rate are reciprocals of each other, which is the whole basis of this calculation.
- Brooks's law
- The observation that adding people to a late software project makes it later, because communication overhead grows faster than output.
Common questions
- Why is the combined time less than the fastest worker alone?
- Because both are contributing at the same time. The fastest worker keeps their whole pace and the second adds on top, so the total can only be quicker than either working alone.
- What is the formula for two people?
- Multiply the two times and divide by their sum. For 6 and 3 hours: (6 × 3) ÷ (6 + 3) = 18 ÷ 9 = 2 hours.
- Can I use this for three or more workers?
- Yes. Add one over each time, then take the reciprocal of the total. The shortcut formula only works for exactly two.
- Does this work for real teams?
- Only roughly. Real work carries coordination costs, and adding people to a late project famously makes it later. Treat the answer as a best case with no overhead.
- How do I handle someone working against the job?
- Enter their time as a negative rate — a drain emptying a tank while taps fill it. If the negative rate is larger, the job never finishes.
- What if one person joins partway through?
- This assumes everyone starts together. For a staggered start, work out how much is left when the second person arrives, then apply the combined rate to the remainder.
- Why does adding a slow worker barely help?
- Because their rate is small. Someone taking 20 hours contributes 1/20 of the job per hour — next to a worker doing 1/5, they add only a fifth as much.