Group Work Calculator

What is Group Work?

Group work is when two or more people work together to complete a task. It's like when you and your friends team up to clean the classroom - you get the job done faster!

How to Calculate Group Work

To figure out how long it takes a group to finish a task, we use a special formula. It's like solving a puzzle with numbers!

Formula

For two people working together, we use this formula:

\[ T = \frac{1}{\frac{1}{a} + \frac{1}{b}} \]

Where:

• \(T\) is the time it takes for the group to complete the work
• \(a\) is the time it takes person A to do the work alone
• \(b\) is the time it takes person B to do the work alone

Calculation Steps

1. Find out how long it takes each person to do the work alone
2. Put these numbers into the formula as \(a\) and \(b\)
3. Calculate \(\frac{1}{a}\) and \(\frac{1}{b}\)
4. Add these fractions together
5. Find the reciprocal of this sum (flip the fraction and calculate)
6. The result is how long it takes the group to finish the work!

Example and Visual Representation

Let's say Amy can paint a fence in 6 hours, and Ben can paint it in 4 hours. How long will it take them working together?

1. Amy: \(a = 6\) hours, Ben: \(b = 4\) hours
2. \(T = \frac{1}{\frac{1}{6} + \frac{1}{4}}\)
3. \(T = \frac{1}{\frac{2}{12} + \frac{3}{12}} = \frac{1}{\frac{5}{12}}\)
4. \(T = \frac{12}{5} = 2.4\) hours

Together, Amy and Ben can paint the fence in just 2.4 hours!