Time and schedule problems

Oct 13, 2025 by wbrum.org 142 views

Introduction

Word problems are an essential part of mathematics, and solving them requires a combination of critical thinking, problem-solving skills, and mathematical knowledge. In this article, we will focus on solving a specific word problem that involves fractions and time. We will break down the problem into smaller steps, explain the mathematical concepts involved, and provide a step-by-step solution.

The Word Problem

One week, a student exercised 2 hours at school and another $\frac{1}{4}$ of an hour at home. If $\frac{1}{6}$ of the total time spent exercising was spent at school, how much time was spent exercising at home?

Understanding the Problem

To solve this problem, we need to understand the given information and what is being asked. The student exercised for a total of 2 hours at school and $\frac{1}{4}$ of an hour at home. We are also given that $\frac{1}{6}$ of the total time spent exercising was spent at school. Our goal is to find the amount of time spent exercising at home.

Step 1: Convert the Time Spent at School to a Fraction

The student exercised for 2 hours at school. To convert this to a fraction, we can use the fact that 1 hour is equal to $\frac{1}{24}$ of a day. Therefore, 2 hours is equal to $2 \times \frac{1}{24} = \frac{1}{12}$ of a day.

Step 2: Convert the Time Spent at Home to a Fraction

The student exercised for $\frac{1}{4}$ of an hour at home. To convert this to a fraction of a day, we can multiply it by $\frac{1}{24}$ , which is the number of hours in a day. Therefore, $\frac{1}{4}$ of an hour is equal to $\frac{1}{4} \times \frac{1}{24} = \frac{1}{96}$ of a day.

Step 3: Find the Total Time Spent Exercising

The total time spent exercising is the sum of the time spent at school and the time spent at home. Therefore, the total time spent exercising is $\frac{1}{12} + \frac{1}{96}$ of a day.

Step 4: Simplify the Fraction

To simplify the fraction, we need to find the least common multiple (LCM) of 12 and 96. The LCM of 12 and 96 is 96. Therefore, we can rewrite the fraction as $\frac{8}{96} + \frac{1}{96} = \frac{9}{96}$ .

Step 5: Find the Time Spent Exercising at Home

We are given that $\frac{1}{6}$ of the total time spent exercising was spent at school. Therefore, the time spent exercising at home is $\frac{5}{6}$ of the total time spent exercising. To find the time spent exercising at home, we can multiply the total time spent exercising by $\frac{5}{6}$ . Therefore, the time spent exercising at home is $\frac{9}{96} \times \frac{5}{6} = \frac{45}{576}$ of a day.

Step 6: Simplify the Fraction

To simplify the fraction, we need to find the greatest common divisor (GCD) of 45 and 576. The GCD of 45 and 576 is 9. Therefore, we can rewrite the fraction as $\frac{5}{64}$ of a day.

Conclusion

In this article, we solved a word problem that involved fractions and time. We broke down the problem into smaller steps, explained the mathematical concepts involved, and provided a step-by-step solution. The final answer is $\frac{5}{64}$ of a day.

Final Answer

Introduction

In our previous article, we solved a word problem that involved fractions and time. In this article, we will provide a Q&A guide to help you understand the concepts and techniques involved in solving word problems.

Q: What is a word problem?

A: A word problem is a mathematical problem that is presented in a real-world context, using words and phrases to describe the situation. Word problems require you to read and understand the problem, identify the key information, and use mathematical concepts and techniques to solve it.

Q: What are some common types of word problems?

A: There are several types of word problems, including:

Measurement problems: These problems involve measuring lengths, weights, or capacities.
Time and schedule problems: These problems involve scheduling events, calculating time intervals, or determining the duration of activities.
Money problems: These problems involve calculating costs, prices, or amounts of money.
Geometry problems: These problems involve calculating areas, perimeters, or volumes of shapes.
Data analysis problems: These problems involve analyzing and interpreting data, such as charts, graphs, or tables.

Q: How do I approach a word problem?

A: To approach a word problem, follow these steps:

Read and understand the problem: Read the problem carefully and make sure you understand what is being asked.
Identify the key information: Identify the key information in the problem, such as numbers, variables, or relationships.
Determine the mathematical concept: Determine the mathematical concept or technique that is required to solve the problem.
Use mathematical concepts and techniques: Use mathematical concepts and techniques to solve the problem.
Check your answer: Check your answer to make sure it is reasonable and accurate.

Q: What are some common mistakes to avoid when solving word problems?

A: Some common mistakes to avoid when solving word problems include:

Misreading the problem: Misreading the problem or misunderstanding the key information.
Not identifying the key information: Not identifying the key information or variables in the problem.
Using the wrong mathematical concept: Using the wrong mathematical concept or technique to solve the problem.
Not checking the answer: Not checking the answer to make sure it is reasonable and accurate.

Q: How can I practice solving word problems?

A: To practice solving word problems, try the following:

Practice with sample problems: Practice solving sample word problems to build your skills and confidence.
Use online resources: Use online resources, such as math websites or apps, to practice solving word problems.
Work with a partner or tutor: Work with a partner or tutor to practice solving word problems and get feedback on your work.
Take online quizzes or tests: Take online quizzes or tests to assess your skills and knowledge.

Q: What are some real-world applications of word problems?

A: Word problems have many real-world applications, including:

Business and finance: Word problems are used in business and finance to calculate costs, prices, and profits.
Science and engineering: Word problems are used in science and engineering to calculate distances, times, and quantities.
Healthcare: Word problems are used in healthcare to calculate medication dosages, treatment times, and patient outcomes.
Education: Word problems are used in education to calculate grades, attendance, and student progress.

Conclusion

In this article, we provided a Q&A guide to help you understand the concepts and techniques involved in solving word problems. We also discussed common mistakes to avoid and provided tips for practicing and improving your skills. By following these tips and practicing regularly, you can become proficient in solving word problems and apply your skills to real-world situations.