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Mathematics

Joint work time

Calculate how long two people or machines need to complete a task together, and what changes when B leaves early.

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01

Your inputs

The starting values are an example.

A value longer than the joint completion time means B stays until the task is finished.

Decimals: 12.5 · Thousands: 1,234.56. Follow the field instructions for lists.

02

Your result

Enter your values and select Calculate.

Your calculation will appear here.

Your result will include the relevant values and units.

Understand the calculation

Formula and example

How it is calculated

Combined rate=1/tA+1/tB. Continuous joint duration=1/(1/tA+1/tB). After B leaves, A completes the remainder.

Worked example

A needs six hours alone and B needs three. Together they take two hours. If B leaves after one hour, the total duration becomes four hours.

Things to check

  • The task must be divisible and the two work rates must add without coordination losses.
  • Setup times, dependencies between steps and declining performance are not modelled.

Frequently asked questions

Why not simply average the times?

The fractions completed per hour are added. Someone who finishes in three hours completes one third each hour; someone who takes six hours completes one sixth.