9. Ramesh Takes 10 Whole 2/5 Minutes To Walk Across The Park. Rajesh Takes 43 Whole 1/5 Who Takes Less And By How Much?10. Ashok Did 1/5 Of The Work Yesterday And Does 1/5 Of Work Today. How Much Work Has He To Do Tomorrow To Complete The Remaining
Mathematical Problem Solving: Understanding Time and Work
In this article, we will delve into two mathematical problems that require us to understand time and work concepts. We will analyze the problems step by step, using mathematical formulas and calculations to arrive at the solutions.
Problem 1: Time Comparison
Ramesh and Rajesh's Walking Time
Ramesh takes 10 whole 2/5 minutes to walk across the park. Rajesh takes 43 whole 1/5 minutes to walk across the park. Who takes less time and by how much?
To compare the time taken by Ramesh and Rajesh, we need to convert the mixed fractions into improper fractions.
- Ramesh's time: 10 2/5 minutes = (10 × 5 + 2)/5 = 52/5 minutes
- Rajesh's time: 43 1/5 minutes = (43 × 5 + 1)/5 = 216/5 minutes
Now, we can compare the two times by finding the difference between them.
- Difference = Rajesh's time - Ramesh's time = (216/5) - (52/5) = (216 - 52)/5 = 164/5 minutes
Since 164/5 minutes is greater than 0, Rajesh takes more time than Ramesh.
To find the difference in time, we can convert the improper fraction back to a mixed fraction.
- Difference = 164/5 minutes = 32 4/5 minutes
Therefore, Ramesh takes less time than Rajesh by 32 4/5 minutes.
Problem 2: Work Completion
Ashok's Work Completion
Ashok did 1/5 of the work yesterday and does 1/5 of the work today. How much work has he to do tomorrow to complete the remaining work?
Let's assume the total work is 1 unit. Ashok has already completed 1/5 of the work, which is 1/5 unit.
- Work completed = 1/5 unit
- Work remaining = 1 - 1/5 = 4/5 unit
Since Ashok does 1/5 of the work today, he has completed an additional 1/5 unit.
- Additional work completed = 1/5 unit
- Total work completed = 1/5 + 1/5 = 2/5 unit
Now, we can find the work remaining to be completed tomorrow.
- Work remaining = 4/5 - 2/5 = 2/5 unit
Therefore, Ashok has to complete 2/5 unit of work tomorrow to complete the remaining work.
Conclusion
In this article, we have analyzed two mathematical problems that require us to understand time and work concepts. We have used mathematical formulas and calculations to arrive at the solutions. By following the step-by-step approach, we have been able to compare the time taken by Ramesh and Rajesh and find the work remaining to be completed by Ashok. These problems demonstrate the importance of mathematical problem-solving skills in real-life scenarios.
Mathematical Problem Solving: Time and Work Q&A
In this article, we will continue to explore mathematical problems related to time and work. We will provide answers to frequently asked questions (FAQs) and provide additional examples to help solidify your understanding of these concepts.
Q: What is the difference between Ramesh and Rajesh's walking time?
A: To find the difference between Ramesh and Rajesh's walking time, we need to convert the mixed fractions into improper fractions.
- Ramesh's time: 10 2/5 minutes = (10 × 5 + 2)/5 = 52/5 minutes
- Rajesh's time: 43 1/5 minutes = (43 × 5 + 1)/5 = 216/5 minutes
Now, we can compare the two times by finding the difference between them.
- Difference = Rajesh's time - Ramesh's time = (216/5) - (52/5) = (216 - 52)/5 = 164/5 minutes
Since 164/5 minutes is greater than 0, Rajesh takes more time than Ramesh.
To find the difference in time, we can convert the improper fraction back to a mixed fraction.
- Difference = 164/5 minutes = 32 4/5 minutes
Therefore, Ramesh takes less time than Rajesh by 32 4/5 minutes.
Q: How much work has Ashok to do tomorrow to complete the remaining work?
A: Let's assume the total work is 1 unit. Ashok has already completed 1/5 of the work, which is 1/5 unit.
- Work completed = 1/5 unit
- Work remaining = 1 - 1/5 = 4/5 unit
Since Ashok does 1/5 of the work today, he has completed an additional 1/5 unit.
- Additional work completed = 1/5 unit
- Total work completed = 1/5 + 1/5 = 2/5 unit
Now, we can find the work remaining to be completed tomorrow.
- Work remaining = 4/5 - 2/5 = 2/5 unit
Therefore, Ashok has to complete 2/5 unit of work tomorrow to complete the remaining work.
Q: What is the formula to find the time taken by two people to complete a task?
A: To find the time taken by two people to complete a task, we can use the following formula:
Time taken by person A = (Work done by person A) / (Rate of work of person A) Time taken by person B = (Work done by person B) / (Rate of work of person B)
We can then compare the two times by finding the difference between them.
Q: How can we find the work remaining to be completed by a person?
A: To find the work remaining to be completed by a person, we can use the following formula:
Work remaining = Total work - Work completed
We can then find the work remaining to be completed by subtracting the work completed from the total work.
Q: What is the importance of mathematical problem-solving skills in real-life scenarios?
A: Mathematical problem-solving skills are essential in real-life scenarios because they help us to:
- Analyze complex problems and break them down into smaller, manageable parts
- Identify patterns and relationships between variables
- Develop critical thinking and problem-solving skills
- Make informed decisions based on data and analysis
By developing strong mathematical problem-solving skills, we can tackle complex problems and make informed decisions in a variety of fields, including business, science, and engineering.
Conclusion
In this article, we have provided answers to frequently asked questions (FAQs) related to time and work. We have also provided additional examples to help solidify your understanding of these concepts. By practicing these problems and developing your mathematical problem-solving skills, you can become more confident and proficient in tackling complex problems in real-life scenarios.