A Dog Won A Race At The Local Fair By Running $13 \frac{1}{4}$ Miles In Exactly 2 Hours. At This Constant Rate, How Long Does It Take The Same Dog To Run The $5 \frac{3}{10}$-mile State Fair Race? Use Ratio Reasoning To

Introduction

In a thrilling display of canine athleticism, a dog has won a local fair race by covering a distance of $13 \frac{1}{4}$ miles in exactly 2 hours. This remarkable feat has left many wondering about the dog's speed and endurance. In this article, we will use ratio reasoning to determine how long it would take the same dog to run the $5 \frac{3}{10}$-mile state fair race at the same constant rate.

Understanding the Dog's Speed

To calculate the time it would take the dog to run the state fair race, we first need to understand the dog's speed. The dog's speed can be calculated by dividing the distance it covered in the local fair race by the time it took to cover that distance. In this case, the distance was $13 \frac{1}{4}$ miles, and the time was 2 hours.

Calculating the Dog's Speed

To calculate the dog's speed, we need to convert the mixed number $13 \frac{1}{4}$ to an improper fraction. We can do this by multiplying the whole number part (13) by the denominator (4), and then adding the numerator (1).

$$13 \frac{1}{4} = \frac{(13 \times 4) + 1}{4} = \frac{52 + 1}{4} = \frac{53}{4}$$

Now that we have the distance in improper fraction form, we can calculate the dog's speed by dividing the distance by the time.

$$\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{53}{4}}{2} = \frac{53}{4} \times \frac{1}{2} = \frac{53}{8}$$

Converting the Dog's Speed to a More Manageable Form

To make the dog's speed easier to work with, we can convert it to a more manageable form by converting the improper fraction to a mixed number.

$$\frac{53}{8} = 6 \frac{5}{8}$$

Calculating the Time for the State Fair Race

Now that we know the dog's speed, we can use it to calculate the time it would take the dog to run the $5 \frac{3}{10}$-mile state fair race. To do this, we need to convert the mixed number $5 \frac{3}{10}$ to an improper fraction.

$$5 \frac{3}{10} = \frac{(5 \times 10) + 3}{10} = \frac{50 + 3}{10} = \frac{53}{10}$$

Now that we have the distance in improper fraction form, we can calculate the time it would take the dog to run the state fair race by dividing the distance by the dog's speed.

$$\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{53}{10}}{\frac{53}{8}} = \frac{53}{10} \times \frac{8}{53} = \frac{8}{10} = \frac{4}{5}$$

Converting the Time to Hours

To make the time easier to understand, we can convert the improper fraction to a decimal.

$$\frac{4}{5} = 0.8$$

Conclusion

In conclusion, using ratio reasoning, we have determined that it would take the dog approximately 0.8 hours, or 48 minutes, to run the $5 \frac{3}{10}$-mile state fair race at the same constant rate as the local fair race. This calculation demonstrates the importance of understanding the dog's speed and using it to make predictions about its performance in future races.

References

• [1] "Mathematics for Dummies". John Wiley & Sons. 2019.
• [2] "Algebra and Trigonometry". Cengage Learning. 2018.

Additional Resources

• [1] Khan Academy. "Mathematics". Khan Academy. 2020.
• [2] Mathway. "Math Problem Solver". Mathway. 2020.

Discussion

Introduction

In our previous article, we calculated the time it would take a dog to run the $5 \frac{3}{10}$-mile state fair race at the same constant rate as the local fair race. In this article, we will answer some frequently asked questions about the dog's speed and endurance.

Q: What is the dog's speed?

A: The dog's speed is $6 \frac{5}{8}$ miles per hour.

Q: How did you calculate the dog's speed?

A: We calculated the dog's speed by dividing the distance it covered in the local fair race ($13 \frac{1}{4}$ miles) by the time it took to cover that distance (2 hours).

Q: What is the distance of the state fair race?

A: The distance of the state fair race is $5 \frac{3}{10}$ miles.

Q: How did you calculate the time it would take the dog to run the state fair race?

A: We calculated the time it would take the dog to run the state fair race by dividing the distance of the state fair race ($5 \frac{3}{10}$ miles) by the dog's speed ($6 \frac{5}{8}$ miles per hour).

Q: What is the time it would take the dog to run the state fair race?

A: The time it would take the dog to run the state fair race is approximately 0.8 hours, or 48 minutes.

Q: Can the dog really run that fast?

A: While dogs are capable of running at high speeds, it's unlikely that a dog could maintain a speed of $6 \frac{5}{8}$ miles per hour for an extended period of time. However, this calculation is purely theoretical and is meant to illustrate the concept of speed and distance.

Q: How can I use this information to calculate the time it would take a dog to run a different distance?

A: To calculate the time it would take a dog to run a different distance, you can use the same formula: Time = Distance / Speed. Simply plug in the distance and speed values, and solve for time.

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

A: This concept has many real-world applications, such as calculating the time it would take a car to travel a certain distance, or determining the time it would take a person to complete a certain task.

Conclusion

In conclusion, we have answered some frequently asked questions about the dog's speed and endurance. We hope this article has provided you with a better understanding of the concept of speed and distance, and how it can be applied in real-world situations.

References

• [1] "Mathematics for Dummies". John Wiley & Sons. 2019.
• [2] "Algebra and Trigonometry". Cengage Learning. 2018.

Additional Resources

• [1] Khan Academy. "Mathematics". Khan Academy. 2020.
• [2] Mathway. "Math Problem Solver". Mathway. 2020.

Discussion

Do you have any questions about the dog's speed and endurance? Share them in the comments below!