Finding the Total Acres Mowed in an Hour

Oct 13, 2025 by wbrum.org 2 views

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. We can calculate this rate by dividing the amount of lawn mowed by the time taken.

Calculating the Rate

Let's calculate the rate at which Walter is mowing the lawn. We know that he takes $\frac{7}{10}$ of an hour to mow $\frac{2}{5}$ of an acre of lawn. To find the rate, we can divide the amount of lawn mowed by the time taken.

Rate = \frac{Amount of lawn mowed}{Time taken}
Rate = \frac{\frac{2}{5} acre}{\frac{7}{10} hour}

To simplify this expression, we can multiply the numerator and denominator by the reciprocal of the denominator.

Rate = \frac{\frac{2}{5} acre}{\frac{7}{10} hour} \times \frac{10}{7}
Rate = \frac{2}{5} \times \frac{10}{7}
Rate = \frac{2 \times 10}{5 \times 7}
Rate = \frac{20}{35}
Rate = \frac{4}{7} acre per hour

Finding the Total Acres 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 acres mowed in an hour. Since we know that Walter takes $\frac{7}{10}$ of an hour to mow $\frac{2}{5}$ of an acre of lawn, we can multiply the rate by the time taken to find the total acres mowed in an hour.

Total acres mowed in an hour = Rate \times Time taken
Total acres mowed in an hour = \frac{4}{7} acre per hour \times 1 hour
Total acres mowed in an hour = \frac{4}{7} acre

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 information provided to calculate the rate at which Walter is mowing the lawn and then used this rate to find the total acres mowed in an hour. The solution to this problem is $\frac{4}{7}$ acre.

Answer

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

Additional Tips and Tricks

When solving problems involving fractions, it's essential to simplify the expressions to make them easier to work with.
To multiply fractions, we can multiply the numerators and denominators separately.
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.

Real-World Applications

This problem has real-world applications in various fields, such as:

Landscaping: This problem can be used to calculate the amount of time and resources required to mow a lawn of a specific size.
Agriculture: This problem can be used to calculate the yield of a crop based on the rate of growth and the time taken to mature.
Construction: This problem can be used to calculate the amount of materials required to build a structure of a specific size.

Conclusion

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

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

Q: How do I calculate the rate at which Walter is mowing the lawn?

A: To calculate the rate at which Walter is mowing the lawn, you need to divide the amount of lawn mowed by the time taken. In this case, the amount of lawn mowed is $\frac{2}{5}$ acre, and the time taken is $\frac{7}{10}$ hour.

Q: How do I simplify the expression for the rate?

A: To simplify the expression for the rate, you can multiply the numerator and denominator by the reciprocal of the denominator. In this case, you can multiply the numerator and denominator by $\frac{10}{7}$ .

Q: How do I find the total acres mowed in an hour?

A: To find the total acres mowed in an hour, you can multiply the rate by the time taken. In this case, the rate is $\frac{4}{7}$ acre per hour, and the time taken is 1 hour.

Q: What is the correct answer to the problem?

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

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as:

Landscaping: This problem can be used to calculate the amount of time and resources required to mow a lawn of a specific size.
Agriculture: This problem can be used to calculate the yield of a crop based on the rate of growth and the time taken to mature.
Construction: This problem can be used to calculate the amount of materials required to build a structure of a specific size.

Q: How do I apply the concept of rate and time to solve similar problems?

A: To apply the concept of rate and time to solve similar problems, you need to follow these steps:

Identify the amount of work done and the time taken to do it.
Calculate the rate at which the work is being done.
Use the rate to find the total amount of work done in a given time period.

Q: What are some common mistakes to avoid when solving problems involving rate and time?

A: Some common mistakes to avoid when solving problems involving rate and time include:

Not simplifying the expressions for the rate and time.
Not using the correct units for the rate and time.
Not multiplying the rate by the time taken to find the total amount of work done.

Q: How do I check my answer to ensure it is correct?

A: To check your answer to ensure it is correct, you can follow these steps:

Review the problem and the solution you have provided.
Check that you have used the correct units for the rate and time.
Check that you have multiplied the rate by the time taken to find the total amount of work done.
Check that your answer is consistent with the information provided in the problem.