Select The Correct Answer.Walter Takes 7 10 \frac{7}{10} 10 7 ​ Of An Hour To Mow 2 5 \frac{2}{5} 5 2 ​ Of An Acre Of Lawn. At This Rate, How Many Acres Will He Mow In An Hour?A. 7 25 \frac{7}{25} 25 7 ​ Acre B. 4 7 \frac{4}{7} 7 4 ​ Acre C. $1

Introduction

In this article, we will delve into a problem that requires us to apply our mathematical skills to find the solution. The problem involves Walter, who takes a certain amount of time to mow a specific portion of an acre of lawn. We will use this information to determine how many acres he can mow in an hour. This problem is a great example of how math is used in real-life scenarios, and it requires us to apply our knowledge of fractions and ratios.

Understanding the Problem

Walter takes $\frac{7}{10}$ of an hour to mow $\frac{2}{5}$ of an acre of lawn. We need to find out how many acres he can mow in an hour. To do this, we need to first understand the rate at which Walter is mowing the lawn. This rate is given by the fraction $\frac{2}{5}$ of an acre per $\frac{7}{10}$ of an hour.

Breaking Down the Problem

To solve this problem, we need to break it down into smaller, more manageable parts. We can start by finding the rate at which Walter is mowing the lawn. This can be done by dividing the amount of lawn mowed ($\frac{2}{5}$ of an acre) by the time taken to mow it ($\frac{7}{10}$ of an hour).

Calculating the Rate

To calculate the rate, we need to divide the amount of lawn mowed by the time taken. This can be done by multiplying the fraction $\frac{2}{5}$ by the reciprocal of the fraction $\frac{7}{10}$.

$\frac{2}{5} \div \frac{7}{10} = \frac{2}{5} \times \frac{10}{7} = \frac{20}{35} = \frac{4}{7}$

So, the rate at which Walter is mowing the lawn is $\frac{4}{7}$ of an acre per hour.

Finding the Total Amount of Lawn Mowed in an Hour

Now that we have the rate at which Walter is mowing the lawn, we can use this information to find the total amount of lawn mowed in an hour. Since the rate is $\frac{4}{7}$ of an acre per hour, we can multiply this rate by the number of hours (1 hour) to find the total amount of lawn mowed.

$\frac{4}{7} \times 1 = \frac{4}{7}$

So, Walter can mow $\frac{4}{7}$ of an acre in an hour.

Conclusion

In this article, we have solved a problem that requires us to apply our mathematical skills to find the solution. We have used the concept of fractions and ratios to determine how many acres Walter can mow in an hour. The solution to this problem is $\frac{4}{7}$ of an acre.

Answer

The correct answer is:

• B. $\frac{4}{7}$ acre

This answer is based on the calculation we performed earlier, which showed that Walter can mow $\frac{4}{7}$ of an acre in an hour.

Additional Tips and Tricks

• When solving problems involving fractions and ratios, it's essential to understand the concept of equivalent ratios.
• To find the rate at which Walter is mowing the lawn, we multiplied the fraction $\frac{2}{5}$ by the reciprocal of the fraction $\frac{7}{10}$.
• To find the total amount of lawn mowed in an hour, we multiplied the rate by the number of hours (1 hour).

Q: What is the rate at which Walter is mowing the lawn?

A: The rate at which Walter is mowing the lawn is $\frac{4}{7}$ of an acre per hour.

Q: How did you calculate the rate?

A: To calculate the rate, we divided the amount of lawn mowed ($\frac{2}{5}$ of an acre) by the time taken to mow it ($\frac{7}{10}$ of an hour). This can be done by multiplying the fraction $\frac{2}{5}$ by the reciprocal of the fraction $\frac{7}{10}$.

Q: What is the total amount of lawn mowed in an hour?

A: The total amount of lawn mowed in an hour is $\frac{4}{7}$ of an acre.

Q: How did you find the total amount of lawn mowed in an hour?

A: We multiplied the rate ($\frac{4}{7}$ of an acre per hour) by the number of hours (1 hour) to find the total amount of lawn mowed.

Q: What is the correct answer to the problem?

A: The correct answer is B. $\frac{4}{7}$ acre.

Q: What are some additional tips and tricks for solving problems involving fractions and ratios?

A: Some additional tips and tricks for solving problems involving fractions and ratios include:

• Understanding the concept of equivalent ratios
• Multiplying fractions by their reciprocals to divide them
• Multiplying rates by the number of hours to find the total amount of work done

Q: How can I improve my problem-solving skills?

A: To improve your problem-solving skills, try the following:

• Practice solving problems involving fractions and ratios
• Review the concepts of equivalent ratios and multiplying fractions by their reciprocals
• Use real-life examples to help you understand the concepts and apply them to solve problems

Q: What are some common mistakes to avoid when solving problems involving fractions and ratios?

A: Some common mistakes to avoid when solving problems involving fractions and ratios include:

• Not understanding the concept of equivalent ratios
• Not multiplying fractions by their reciprocals to divide them
• Not multiplying rates by the number of hours to find the total amount of work done

By following these tips and avoiding common mistakes, you can improve your problem-solving skills and become more confident in your ability to tackle math problems.

Conclusion

In this article, we have answered some frequently asked questions about the mowing problem. We have provided step-by-step solutions to the problem and offered additional tips and tricks for solving problems involving fractions and ratios. By following these tips and avoiding common mistakes, you can improve your problem-solving skills and become more confident in your ability to tackle math problems.

Additional Resources

• For more information on fractions and ratios, check out our article on [Fractions and Ratios](link to article).
• For more practice problems involving fractions and ratios, try our [Practice Problems](link to practice problems) section.
• For more tips and tricks on problem-solving, check out our [Problem-Solving Tips](link to problem-solving tips) section.