Work Rate Combined Time Calculator
If one worker finishes a job in A hours and another in B hours, how long together? Solve the classic work-rate problem instantly.
How it works
Combined time = 1 ÷ (1/t₁ + 1/t₂) = (t₁ · t₂) ÷ (t₁ + t₂)
Rates add, times do not. Each worker completes a fraction of the job per hour — 1/t of it — so working together their rates sum, and the combined time is the reciprocal of that sum. The result is always shorter than the faster worker alone, because a second pair of hands can only speed things up, never slow them down.
Worked example
Worker 1 does the job in 4 hours (rate 1/4 per hour); worker 2 in 6 hours (rate 1/6). Together the rate is 1/4 + 1/6 = 5/12 of the job per hour, so the time is 12/5 = 2.4 hours — that is 2 hours 24 minutes, faster than either alone.
Frequently asked questions
Why can’t I just average the two times?
Averaging times (4 and 6 → 5 hours) is wrong because it ignores that both are working at once. You add their rates instead, which always gives a time shorter than the faster worker on their own.
What if both workers take the same time?
If each takes t hours alone, together they take t/2 — exactly half — because two equal rates double the output. The formula gives (t·t)/(t+t) = t/2.
Does this apply to pipes filling a tank?
Yes. It is the same maths whenever two agents work on one task at steady rates — pipes filling a pool, printers on a job, or hoses draining a tank. For a draining pipe, use a negative rate.
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This calculator is for educational purposes. Double-check important results before acting on them.