Edward Walks At A Pace Of $2 \frac{1}{4}$ Miles In $\frac{2}{3}$ Hour. How Many Miles Does Edward Walk Per Hour?A. $1 \frac{1}{2}$ Miles Per Hour B. $4 \frac{1}{2}$ Miles Per Hour C. $3 \frac{3}{8}$ Miles

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Introduction

In this article, we will delve into the world of mathematics and explore the concept of speed. Specifically, we will analyze the walking speed of Edward, who walks at a pace of 2142 \frac{1}{4} miles in 23\frac{2}{3} hour. Our goal is to determine how many miles Edward walks per hour.

Understanding the Problem

To solve this problem, we need to understand the concept of speed, which is defined as the distance traveled per unit of time. In this case, we are given the distance traveled by Edward, which is 2142 \frac{1}{4} miles, and the time taken, which is 23\frac{2}{3} hour. We need to find the speed at which Edward walks, which is the distance traveled per hour.

Converting Mixed Numbers to Improper Fractions

Before we can proceed with the calculation, we need to convert the mixed number 2142 \frac{1}{4} to an improper fraction. To do this, we multiply the whole number part (2) by the denominator (4), and then add the numerator (1). This gives us:

214=(2×4)+14=8+14=942 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}

Converting the Time to a Common Denominator

We also need to convert the time 23\frac{2}{3} hour to a common denominator with the distance traveled. To do this, we multiply the numerator and denominator of the time by 4, which gives us:

23=2×43×4=812\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}

Calculating the Speed

Now that we have converted the distance and time to improper fractions, we can calculate the speed at which Edward walks. To do this, we divide the distance traveled by the time taken:

Speed=DistanceTime=94812=94×128=9×124×8=10832\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{9}{4}}{\frac{8}{12}} = \frac{9}{4} \times \frac{12}{8} = \frac{9 \times 12}{4 \times 8} = \frac{108}{32}

Simplifying the Fraction

We can simplify the fraction 10832\frac{108}{32} by dividing both the numerator and denominator by their greatest common divisor, which is 4. This gives us:

10832=108÷432÷4=278\frac{108}{32} = \frac{108 \div 4}{32 \div 4} = \frac{27}{8}

Converting the Fraction to a Mixed Number

Finally, we can convert the improper fraction 278\frac{27}{8} to a mixed number by dividing the numerator by the denominator:

278=338\frac{27}{8} = 3 \frac{3}{8}

Conclusion

In conclusion, Edward walks at a pace of 3383 \frac{3}{8} miles per hour.

Answer

The correct answer is:

Introduction

In our previous article, we analyzed the walking speed of Edward, who walks at a pace of 2142 \frac{1}{4} miles in 23\frac{2}{3} hour. We determined that Edward walks at a pace of 3383 \frac{3}{8} miles per hour. In this article, we will answer some frequently asked questions related to this topic.

Q&A

Q: What is the formula to calculate speed?

A: The formula to calculate speed is:

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator, and then add the numerator. For example, to convert 2142 \frac{1}{4} to an improper fraction, you would multiply 2 by 4, and then add 1:

214=(2×4)+14=8+14=942 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, you divide the numerator by the denominator. For example, to convert 278\frac{27}{8} to a mixed number, you would divide 27 by 8:

278=338\frac{27}{8} = 3 \frac{3}{8}

Q: What is the difference between speed and velocity?

A: Speed and velocity are related but distinct concepts. Speed is a scalar quantity that refers to the rate at which an object moves, while velocity is a vector quantity that refers to the rate at which an object moves in a specific direction. In the context of our previous article, we were calculating speed, not velocity.

Q: How do I calculate the distance traveled by an object?

A: To calculate the distance traveled by an object, you can use the formula:

Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}

Q: What is the relationship between speed, distance, and time?

A: The relationship between speed, distance, and time is given by the formula:

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

This formula shows that speed is equal to the distance traveled divided by the time taken.

Conclusion

In conclusion, we have answered some frequently asked questions related to the walking speed of Edward. We hope that this article has been helpful in clarifying any doubts you may have had.

Additional Resources

For more information on speed, distance, and time, we recommend the following resources:

  • Khan Academy: Speed and Velocity
  • Math Is Fun: Speed and Velocity
  • Wikipedia: Speed and Velocity

Answer Key

The correct answers to the questions are:

  1. The formula to calculate speed is: Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}
  2. To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator, and then add the numerator.
  3. To convert an improper fraction to a mixed number, you divide the numerator by the denominator.
  4. Speed and velocity are related but distinct concepts.
  5. To calculate the distance traveled by an object, you can use the formula: Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}
  6. The relationship between speed, distance, and time is given by the formula: Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}