Calculating the Missing Value

Oct 13, 2025 by miodeya.com 106 views

The Power of Collaboration: Understanding Work Rates and Time

In the world of mathematics, understanding work rates and time is crucial in solving problems that involve collaboration and individual efforts. The scenario presented in this article is a classic example of how two individuals, Alex and Millie, work together to complete a task. In this case, they are filing papers in file cabinets. We will explore the concept of work rates, time, and how to calculate the missing value in the table that represents the part of the papers that Alex would file if he were to work alone.

Work rate is a measure of how much work an individual can complete in a given amount of time. It is usually expressed as a fraction of the total work, with the numerator representing the amount of work completed and the denominator representing the time taken to complete that work. In the context of the problem, Alex and Millie's combined work rate is 1/4, meaning they can complete the entire task in 4 hours.

We are given that it would have taken Alex 6 hours to complete the task alone. This means that Alex's work rate is 1/6, as he can complete the entire task in 6 hours. To find the fraction of the task that Alex completes in 1 hour, we can divide his work rate by 1:

Alex's Work Rate per Hour

1/6 (Alex's work rate) ÷ 1 (hour) = 1/6

This means that Alex can complete 1/6 of the task in 1 hour.

Since Alex and Millie's combined work rate is 1/4, and Alex's work rate is 1/6, we can find Millie's work rate by subtracting Alex's work rate from the combined work rate:

Millie's Work Rate

1/4 (Combined work rate) - 1/6 (Alex's work rate) = 1/12

This means that Millie can complete 1/12 of the task in 1 hour.

The table below represents the part of the papers that Alex would file if he were to work alone. We need to find the missing value in the table.

Time (hours)	Part of Papers Alex Would File
1	1/6
2	2/6
3	3/6
4	4/6
5	5/6
6	6/6

To find the missing value, we can calculate the fraction of the task that Alex completes in 1 hour, which is 1/6. We can then multiply this fraction by the number of hours to find the part of the papers that Alex would file in that time.

Calculating the Missing Value

1/6 (Alex's work rate per hour) × 1 (hour) = 1/6
1/6 (Alex's work rate per hour) × 2 (hours) = 2/6
1/6 (Alex's work rate per hour) × 3 (hours) = 3/6
1/6 (Alex's work rate per hour) × 4 (hours) = 4/6
1/6 (Alex's work rate per hour) × 5 (hours) = 5/6
1/6 (Alex's work rate per hour) × 6 (hours) = 6/6

The missing value in the table is 5/6, which represents the part of the papers that Alex would file if he were to work alone for 5 hours.

In conclusion, understanding work rates and time is crucial in solving problems that involve collaboration and individual efforts. By calculating Alex's work rate and Millie's work rate, we can find the missing value in the table that represents the part of the papers that Alex would file if he were to work alone. This problem is a classic example of how mathematics can be applied to real-world scenarios to solve problems and make informed decisions.
Frequently Asked Questions: Understanding Work Rates and Time

In our previous article, we explored the concept of work rates and time, and how to calculate the missing value in the table that represents the part of the papers that Alex would file if he were to work alone. In this article, we will answer some frequently asked questions related to work rates and time.

A: Work rate is a measure of how much work an individual can complete in a given amount of time. It is usually expressed as a fraction of the total work, with the numerator representing the amount of work completed and the denominator representing the time taken to complete that work.

A: To calculate work rate, you need to know the amount of work completed and the time taken to complete that work. You can then express the work rate as a fraction, with the numerator representing the amount of work completed and the denominator representing the time taken to complete that work.

A: Work rate and time are related but distinct concepts. Work rate refers to the amount of work completed in a given amount of time, while time refers to the duration of the work. For example, if you can complete 1/2 of a task in 2 hours, your work rate is 1/2, but the time taken to complete the task is 2 hours.

A: To calculate the time taken to complete a task, you need to know the amount of work completed and the work rate. You can then use the formula:

Time = Amount of work completed ÷ Work rate

For example, if you can complete 1/2 of a task in 2 hours, the time taken to complete the task is:

Time = 1/2 ÷ 1/2 = 1 hour

A: Work rate and efficiency are related but distinct concepts. Efficiency refers to the ability to complete a task with minimal waste and maximum productivity, while work rate refers to the amount of work completed in a given amount of time. For example, if you can complete a task in 2 hours with 100% efficiency, your work rate is 1/2, but if you can complete the same task in 1 hour with 100% efficiency, your work rate is 1/1.

A: To calculate the work rate of a team, you need to know the amount of work completed by each team member and the time taken to complete that work. You can then express the team's work rate as a fraction, with the numerator representing the amount of work completed and the denominator representing the time taken to complete that work.

A: Work rate and productivity are related but distinct concepts. Productivity refers to the ability to complete a task with minimal waste and maximum productivity, while work rate refers to the amount of work completed in a given amount of time. For example, if you can complete a task in 2 hours with 100% productivity, your work rate is 1/2, but if you can complete the same task in 1 hour with 100% productivity, your work rate is 1/1.

In conclusion, understanding work rates and time is crucial in solving problems that involve collaboration and individual efforts. By answering these frequently asked questions, we hope to have provided a better understanding of the concepts of work rate and time.