Work Rate Calculator

This work rate calculator works out how long two people or machines take to finish a job when they work together, using the trick of adding rates rather than averaging times. Enter how long each one takes to complete the job alone, in any matching unit such as hours, days or minutes, and the calculator returns the combined rate, shown as jobs completed per unit time, plus the time it takes them to finish together in a plain result line such as "Together: 2.4 time units." Behind the scenes each worker's speed is treated as a fraction of the job done per unit time; those two fractions are added to get the combined rate, then the reciprocal gives the joint time, which is always shorter than either one alone. This suits painting, laying pipe, filling a tank, writing code or any shared task, whether you are checking a textbook problem, planning a roster, or estimating how fast a joint effort finishes. Change either time and the result updates instantly. The same method extends to three or more workers by adding all their rates before taking the reciprocal, a shortcut covered in the FAQs below alongside a worked example using the default values of 4 and 6 hours. Results are rounded for display, so treat the answer as a close approximation rather than an exact figure.

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Time alone, A

Time alone, B

Together: 2.4 time units

Combined rate (jobs per unit)0.416667

Time together2.4

The formula

If A takes time a and B takes time b, their rates are 1/a and 1/b jobs per unit time. The combined rate is 1/a + 1/b, and the time together is the reciprocal: 1 / (1/a + 1/b).

Worked example

If A takes 4 hours and B takes 6 hours, the combined rate is 1/4 + 1/6 = 5/12 of the job per hour, so together they take 12/5 = 2.4 hours. Enter 4 and 6 to confirm.

Frequently asked questions

Why not just average the times?

Because rates add, not times. You add the fractions of the job each does per unit time, then take the reciprocal.

Will the joint time always be shorter?

Yes. Two workers together finish faster than either alone, so the combined time is less than the smaller of the two.

Can I extend it to three workers?

Yes, add all three rates (1/a + 1/b + 1/c) and take the reciprocal.

Who this calculator is for

This calculator is for students, programmers and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid input.
The standard algorithm is applied.
Results are rounded for display.

Formula and sources

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