Formula
Rate of a worker = 1 ÷ (days alone)Together: days = 1 ÷ (1/a + 1/b + 1/c)Other worker: 1/b = 1/t − 1/a
- One whole job = 1
Add the work each person does in one day, then divide 1 by that sum.
Worked example
A in 10 days, B in 15 days
- What do you want to find?
- Days to finish together (2–3 workers)
- Worker A alone (days)
- 10 days
- Worker B alone (days)
- 15 days
Days to finish together
6 days
Combined work per day: 16.6667%
How it works
If A can finish a job in 10 days and B in 15, A does 1/10 of it per day and B does 1/15. Together they do 1/10 + 1/15 = 1/6 per day, so the whole job takes 6 days. Each worker's share of the finished job is in proportion to their daily rate.
The same rate method works for pipes filling a tank (a draining pipe has a negative rate) and for any shared task. If A starts alone and B joins later, the tool works out how much is left when B arrives and divides by the combined rate. For proportion-style problems with men and days use Proportion Calculator (inverse mode).
Assumptions and limits
- Every worker is assumed to work at a constant rate and not get in each other's way.
Related tools
Proportion CalculatorSolve for the missing value in direct or inverse proportion (A/B = C/D).Speed, Time and Distance CalculatorFind speed, time or distance when you know the other two, in your choice of units.Fraction CalculatorAdd, subtract, multiply and divide fractions and mixed numbers, simplified automatically.Ratio CalculatorSimplify a ratio to lowest terms, or split an amount in a given ratio.HCF and LCM CalculatorHighest common factor (GCD) and lowest common multiple of two or more numbers, with prime factors.