Determining the Time B Takes to Copy 26 Pages: An In-Depth Analysis

In this article, we will explore how to determine the time it takes for B to copy 26 pages given the work rates of A and the combined work rate of A and B. This kind of productivity calculation is crucial for understanding and optimizing the efficiency of team collaboration and individual contributions.

Understanding the Problem

Let's first understand the given conditions:

A can copy 50 pages in 10 hours. A and B together can copy 70 pages in 10 hours.

We need to find how long B would take to copy 26 pages individually.

Calculating Individual and Combined Rates

To solve this problem, we will calculate the individual and combined work rates of A and B.

Rate of A

The rate of A in terms of pages per hour can be calculated as follows:

Rate of A (frac{50 ,text{pages}}{10 ,text{hours}} 5 ,text{pages per hour})

Combined Rate of A and B

The combined rate of A and B together is:

Rate of A and B (frac{70 ,text{pages}}{10 ,text{hours}} 7 ,text{pages per hour})

Rate of B

Now, to find the rate of B, we subtract the rate of A from the combined rate of A and B:

Rate of B (text{Rate of A and B} - text{Rate of A} 7 ,text{pages per hour} - 5 ,text{pages per hour} 2 ,text{pages per hour})

Time for B to Copy 26 Pages

With the rate of B known, we can calculate the time it would take B to copy 26 pages:

Time (frac{text{Pages}}{text{Rate}} frac{26 ,text{pages}}{2 ,text{pages per hour}} 13 ,text{hours})

Conclusion

Therefore, B takes 13 hours to copy 26 pages. This analysis helps in understanding the efficiency of individual and combined work rates, which is essential for optimizing productivity in any work environment. Whether you're managing a team or evaluating individual performance, the ability to calculate and understand work rates is a valuable skill.