Shared Work Calculator

Understanding Shared Work Calculations

What is Shared Work?

Shared work refers to a situation where multiple people work together to complete a task. The shared work principle is used to calculate how long it will take for a group of people to finish a job when working simultaneously.

The Shared Work Formula

The formula for calculating the time it takes to complete a shared task is:

\[T = \frac{1}{\sum_{i=1}^n \frac{1}{T_i}}\]

Where:

• \(T\) is the time it takes to complete the task together
• \(T_i\) is the time it takes for person i to complete the task alone
• \(n\) is the number of people working together

Calculation Steps

To calculate the shared work time:

1. Determine the time it takes each person to complete the task individually
2. Take the reciprocal of each individual time
3. Sum up all the reciprocals
4. Take the reciprocal of the sum to get the final shared time

Example Calculation

Let's say Person A can complete a task in 4 hours, and Person B can complete the same task in 6 hours. How long will it take them to complete the task together?

\[T = \frac{1}{\frac{1}{4} + \frac{1}{6}} = \frac{1}{\frac{3}{12} + \frac{2}{12}} = \frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4\text{ hours}\]

Visual Representation

This diagram shows the time it takes each person individually (blue and red) and the time it takes them working together (green).