Solving Work Rate Problems: Men, Women, and Children Working Together

In this article, we delve into the fascinating world of work rate problems, focusing on the collaboration dynamics between men, women, and children. We'll explore how to solve complex problems with multiple variables, using a real-world example. By the end, you'll understand the crucial role of work rates and be equipped to tackle similar challenges effectively.

Understanding Work Rates

A work rate problem involves determining the efficiency of different individuals or teams working together to complete a task.

Step 1: Determine Work Rates

Let's start by understanding the work rate for each individual group.

Men: Two men can complete a piece of work in 3 days. Women: Three women can complete the same work in 4 days. Children: Four children can complete the same work in 6 days.

We'll calculate the work done by each group in one day to find their work rates.

Calculation of Work Rates

For men:

Two men can complete the work in 3 days. Work done by 2 men in 1 day 1/3 Work done by 1 man in 1 day 1/3 ÷ 2 1/6

For women:

Three women can complete the work in 4 days. Work done by 3 women in 1 day 1/4 Work done by 1 woman in 1 day 1/4 ÷ 3 1/12

For children:

Four children can complete the work in 6 days. Work done by 4 children in 1 day 1/6 Work done by 1 child in 1 day 1/6 ÷ 4 1/24

Step 2: Combine Work Rates

Now we need to find the combined work rate of 1 man, 1 woman, and 2 children. We'll add their individual work rates.

Work done by 1 man in 1 day 1/6 Work done by 1 woman in 1 day 1/12 Work done by 2 children in 1 day 2 × 1/24 1/12 Total work done in 1 day 1/6 1/12 1/12

To add these fractions, we need a common denominator. The least common multiple of 6 and 12 is 12.

Convert 1/6 to twelfths: 1/6 2/12 Now we can add: 2/12 1/12 1/12 4/12 1/3

The combined work rate of 1 man, 1 woman, and 2 children is 1/3 of the work per day.

Step 3: Calculate the Time to Complete the Work

To find the time taken to complete 1 whole work, we take the reciprocal of the combined work rate.

Time taken 1 / (1/3) 3 days

Therefore, 1 man, 1 woman, and 2 children can complete the work in 3 days.

Conclusion

We have successfully determined the time it takes for 1 man, 1 woman, and 2 children to complete a piece of work. This method can be applied to various real-world scenarios, helping us optimize productivity and resource allocation.

Related Keywords

In addition to the work rate problem, our discussion covers the concepts of productivity and time to complete work, which are essential in fields such as project management and human resources.

Related Keywords: work rate, productivity, time to complete work