Collaborative Efficiency in Task Completion: A Case of Sandy and Claude Painting a Fence

In any work environment, understanding the dynamics of team collaboration and individual contributions is crucial. This article delves into a relatable scenario involving Sandy and Claude, who are tasked to paint a fence. The analysis showcases how their combined efforts can enhance overall productivity and achieve tasks more efficiently.

Introduction to the Scenario

Imagine Sandy, who takes 3 hours to paint a fence, and Claude, who takes 6 hours for the same job. The question at hand is: How long will it take for both of them working together to complete the fence?

Understanding Work Rates

To solve this problem, we need to understand the concept of work rates. Work rate is typically expressed as the amount of work completed per unit of time. In this context, it means the proportion of the fence that each individual can paint in one hour.

Sandy’s Work Rate: Since Sandy can paint the entire fence in 3 hours, her work rate is 1/3 of the fence per hour.

Claude’s Work Rate: Claude, on the other hand, can paint the entire fence in 6 hours, making his work rate 1/6 of the fence per hour.

Combining Work Rates

When two individuals work together, their combined work rate is the sum of their individual work rates. Therefore, we add Sandy’s and Claude’s work rates.

Total Work Rate Together: Sandy and Claude, working together, will paint (1/3 1/6) of the fence per hour.

1/3 1/6 2/6 1/6 3/6 3/6 1/2 of the fence per hour.

This means that together, they paint half of the fence in one hour. Therefore, to complete the entire fence, it will take them two hours.

Verification with Numerical Representation

To further verify, let's represent the fence with numerical data. Suppose the fence is 90 feet long.

Sandy: In 2 hours, Sandy can paint 2 × 30 feet 60 feet (30 feet per hour). Claude: In 2 hours, Claude can paint 2 × 15 feet 30 feet (15 feet per hour).

Thus, in 2 hours, Sandy completes 60 feet, and Claude completes 30 feet, making a total of 90 feet, which is the entire fence.

Conclusion

The analysis clearly shows that by working together, Sandy and Claude can complete the job in two hours. This demonstrates the significant benefits of collaboration and the importance of understanding individual work rates in team settings. Whether in a paint shop or any other collaborative environment, harnessing the strengths of each member can lead to better outcomes and increased efficiency.

Key Takeaways:

Individual work rates determine the pace of task completion. Combining individual work rates provides a combined work rate. Effective collaboration can significantly reduce the time needed to complete tasks.