Collaborative Project Completion: John and Sarah’s Efficient Teamwork

Introduction

John and Sarah are two highly efficient workers. While John can complete a project in 12 days on his own, Sarah can do the same job in just 8 days. This article explores how their combined efforts would impact the completion time when they work in tandem. We delve into the math behind collaborative project completion using their individual work rates and derive the equation to determine the days required for both to finish the project together.

Understanding Individual Work Rates

To begin with, let's establish the work rates for John and Sarah.

John's Work Rate:
John can complete a project in 12 days. Therefore, his daily work rate is 1/12 of the project.

Sarah's Work Rate:
Sarah can complete the same project in only 8 days. Hence, her daily work rate is 1/8 of the project.

Combined Work Rate Calculation

When working together, their combined work rate is the sum of their individual work rates:

Combined Work Rate:
Combined work rate

Therefore, together, they complete 5/24 of the project in one day.

Calculation of Total Days Required

To find out the total number of days required for John and Sarah to complete the project together, we use the following equation:

Total Days:
Total days 1 ÷ (5/24) 24/5 4.8 days

In decimal form, 4.8 days can be broken down into 4 days, 19 hours, and 12 minutes. Therefore, working together, John and Sarah can complete the project in 4 days, 19 hours, and 12 minutes.

Verification of Solution

Let's verify the solution by breaking down the total work into smaller units and confirming that the work rate calculation adds up:

Verification:
If they work together for 4.8 days, then in one day they complete 5/24 of the project. Therefore, in 4.8 days, they complete:

5/24 × 4.8 5/24 × 4 5/24 × 0.8 20/24 4/24 24/24 1

This confirms that John and Sarah can complete the project in 4.8 days when working together.

Conclusion

Through an efficient and collaborative effort, John and Sarah can reduce the project completion time significantly. By understanding the combined work rate, they can plan and manage their tasks more effectively, ensuring timely project delivery. Whether you're a project manager or a collaborator, understanding work rate math is crucial for optimizing team performance.