Efficient Workforce Collaboration: A Real-Life Example of Joint Productivity

Collaboration among team members is crucial for efficient work completion. This article delves into the joint productivity of three individuals—Ankit, Vinod, and Chetan—each with different work rates. By understanding their individual contributions and how they combine, we can calculate the total time required for the group to complete a piece of work together. This example not only highlights the importance of individual work rates but also showcases the benefits of team synergy in overcoming work challenges.

Individual Work Rates

Let's start by calculating the individual work rates of Ankit, Vinod, and Chetan to understand their respective contributions to the project.

Ankit's Work Rate

Step 1: Calculating Ankit's work rate.

Ankit can complete ( frac{1}{3} ) of the work in 5 days. Therefore, his rate is:

( text{Ankit's rate} frac{frac{1}{3}}{5} frac{1}{15} text{ work/day} )

Vinod's Work Rate

Step 1: Calculating Vinod's work rate.

Vinod can complete ( frac{3}{5} ) of the work in 15 days. Therefore, his rate is:

( text{Vinod's rate} frac{frac{3}{5}}{15} frac{3}{75} frac{1}{25} text{ work/day} )

Chetan's Work Rate

Step 1: Calculating Chetan's work rate.

Chetan can complete ( frac{6}{7} ) of the work in 18 days. Therefore, his rate is:

( text{Chetan's rate} frac{frac{6}{7}}{18} frac{6}{126} frac{1}{21} text{ work/day} )

Combined Work Rate

Step 2: Combining their work rates.

Now we add their work rates together to find the combined work rate:

( text{Combined rate} text{Ankit's rate} text{Vinod's rate} text{Chetan's rate} )

( text{Combined rate} frac{1}{15} frac{1}{25} frac{1}{21} )

Finding a Common Denominator

Step 3: Finding a common denominator.

The least common multiple (LCM) of 15, 25, and 21 is 105. Now we convert each fraction to have this common denominator:

( frac{1}{15} frac{7}{105} )

( frac{1}{25} frac{4.2}{105} text{ (approximately but let's keep it as a fraction)} → frac{21}{525} frac{4.2}{105} → frac{21}{525} frac{4.2}{105} )

( frac{1}{21} frac{5}{105} )

Now summing these:

( frac{7}{105} frac{4.2}{105} frac{5}{105} frac{16.2}{105} )

Calculating the Time to Complete the Work

Step 4: Calculating the time to complete the work.

The combined work rate is:

( frac{16.2}{105} text{ work/day} )

To find the time ( T ) taken to complete 1 work unit:

( T frac{1 text{ work}}{text{Combined rate}} frac{1}{frac{16.2}{105}} frac{105}{16.2} approx 6.48 text{ days} )

Conclusion

Therefore, Ankit, Vinod, and Chetan working together will complete the work in approximately 6.48 days.

Alternative Calculation Method

Alternatively, we can use a simpler formula to calculate the combined work rate of the team. If A, B, and C can complete a work in ( X, Y, ) and ( Z ) days respectively, then they together can complete the work in:

( frac{XYZ}{XY YZ ZX} text{ days} )

Applying this formula:

>User's alternative calculation method: Ankit can complete the whole work in 5x3/115 days.

Vinod can complete the whole work in 15X 5/3 25 days.

Chetan can complete the whole work in 18 x 7/6 21 days

So all the THREE can complete the work together in:

( frac{15 times 25 times 21}{15 25 21} 6.48 text{ days} )

Thus, the time taken for the team to complete the work together is 6.48 days.

Explanation

This method is based on the principle that the combined rate of work is the sum of individual rates, and the time taken to complete the work is the reciprocal of the combined rate. This demonstrates the efficiency of using a team to address a common task, where the rates can be added and the time taken to complete the work calculated using a simple formula.