Collaboration Efficiency: How Ravi and Kumar Can Type 110 Pages Together

In any collaborative project, understanding the combined efficiency of team members is crucial. This article explores a practical example – how Ravi and Kumar can efficiently type 110 pages together. Through step-by-step calculations, we will determine their individual typing rates and then combine these rates to find the time required for the task.

Introduction to Typing Rates

Let's start by breaking down the problem. Ravi takes 6 hours to type 32 pages, while Kumar takes 5 hours to type 40 pages. By calculating their individual typing rates, we can understand how much they can complete in a single hour. This information will help us determine the combined efficiency and the total time required for the assignment.

Step 1: Determine Individual Typing Rates

The first step is to calculate the typing rates for both Ravi and Kumar.

Ravi's Typing Rate

Ravi types 32 pages in 6 hours. Therefore, his typing rate is:

Rate_{Ravi} frac{32 text{ pages}}{6 text{ hours}} frac{16}{3} text{ pages per hour}

This is approximately 5.33 pages per hour.

Kumar's Typing Rate

Kumar types 40 pages in 5 hours. Thus, his typing rate is:

Rate_{Kumar} frac{40 text{ pages}}{5 text{ hours}} 8 text{ pages per hour}

Step 2: Combine Typing Rates

Now, we need to find their combined typing rate. By adding their individual rates, we can determine how much they can type together in one hour.

Combined Typing Rate

The combined rate is calculated by adding their individual rates:

Combined Rate Rate_{Ravi} Rate_{Kumar} frac{16}{3} 8

To add these, we convert 8 to a fraction:

8 frac{24}{3}

Now, we add the fractions:

Combined Rate frac{16}{3} frac{24}{3} frac{40}{3} text{ pages per hour}

This is approximately 13.33 pages per hour.

Step 3: Calculate the Total Time Required

With their combined typing rate, we can now determine the time required to type 110 pages. The formula to find the time is:

Time frac{Total Pages}{Combined Rate} frac{110 text{ pages}}{frac{40}{3} text{ pages per hour}} 110 times frac{3}{40} frac{330}{40} 8.25 text{ hours}

This means that Ravi and Kumar will take 8.25 hours to type 110 pages together, which is 8 hours and 15 minutes.

Conclusion

In this project, Ravi and Kumar's combined efficiency allows them to type 110 pages in a total of 8 hours and 15 minutes. This example highlights the importance of understanding individual and combined work rates in collaborative settings. By optimizing their efforts, they can effectively manage time and resources, enhancing overall efficiency.