Understanding Collaborative Work Efficiency in Fewer Days

When dealing with work efficiency and collaborative efforts, it's essential to understand how different individuals or teams work together to complete a task. This article explores a specific problem where two individuals, A and B, can complete a task in 15 days and 12 days, respectively. We will analyze how much work they can complete together in 3 days, providing step-by-step solutions and clear explanations.

Problem Analysis: A and B's Work Efficiency

Let's analyze the given scenario:

Individually, How Much Work Can A and B Complete?

Given:

A can complete the work in 15 days. B can complete the work in 12 days.

This means:

Work done by A in 1 day 1/15 (or approximately 0.0667) Work done by B in 1 day 1/12 (or approximately 0.0833)

Combined Work Rate

To find the combined work rate, add the individual work rates:

Combined work rate in 1 day (1/15) (1/12) 4/60 5/60 9/60

This can be simplified to:

Combined work rate in 1 day 9/60, which simplifies further to 3/20

Calculating Work Done in 3 Days

Now, to find out how much work A and B can complete together in 3 days:

Work done in 3 days 3 days * (3/20) 9/20

Thus, A and B working together can complete 9/20 (or 45%) of the work in 3 days.

Alternative Approach: Using Percentages

An alternative method involves using the efficiency percentages:

Step-by-step Calculation

1. Find the daily work efficiency:

Efficiency of A in 1 day 100/15 8.3333% Efficiency of B in 1 day 100/12 6.6667%

2. Combined efficiency in 1 day:

Combined efficiency 8.3333% 6.6667% 15% (approx.)

3. Combined efficiency in 3 days:

3 days * 15% 45% which is 45/100 0.45 in decimal form. This can be simplified to 9/20 when expressed as a fraction.

Conclusion and Real-world Application

This analysis shows how to efficiently calculate the amount of work done by a team over a specific period. Understanding these concepts can be particularly useful in managing projects and ensuring that tasks are completed within the stipulated time frame. Whether you use decimals or fractions, the key is clear and logical reasoning.