Productivity

Productivity (rate of work) is a measure of how much work is completed per unit time. If $A$ is the total work, $t$ is the time, and $N$ is productivity, then $N = \frac{A}{t}$. For joint work, if several workers or machines work together, their individual productivities add: $N_{\text{total}} = N_1 + N_2 + \dots + N_k$. The time to complete a task is $t = \frac{A}{N}$. Problems often involve finding one of these quantities given the others, or analyzing combined rates (joint work).

Important properties

• Productivity is work per unit time: $N = \frac{A}{t}$.

• Time to complete work: $t = \frac{A}{N}$.

• Work done in a given time: $A = N \times t$.

• For joint work, total productivity is the sum of individual productivities.

• If a worker or machine removes work (like draining a pool), its productivity is negative in the sum.