Applying the Formula to the Situation

Oct 13, 2025 by sorusgentrification.com 17 views

Understanding the Problem

When a giraffe runs at a rate of 32 miles per hour, we can use the concept of speed to determine the distance it covers in a given time. The speed of the giraffe is given as 32 miles per hour, and we need to find an equation that models this situation. In this article, we will explore the relationship between time, speed, and distance to determine the correct equation.

The Concept of Speed

Speed is a measure of how fast an object is moving. It is typically measured in units of distance per unit of time, such as miles per hour or kilometers per hour. In this case, the speed of the giraffe is 32 miles per hour, which means that it covers a distance of 32 miles in one hour.

The Relationship Between Time, Speed, and Distance

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

Distance = Speed × Time

This formula can be represented mathematically as:

d = rt

where d is the distance, r is the speed, and t is the time.

Applying the Formula to the Situation

In this case, the speed of the giraffe is 32 miles per hour, and we want to find the distance it covers in a given time. We can use the formula d = rt to model this situation. Let's substitute the given values into the formula:

d = 32t

where d is the distance and t is the time.

Analyzing the Options

Now that we have the equation d = 32t, let's analyze the options given:

A. 32h = d B. 32d = h C. d = 32t

Option A is incorrect because it does not represent the correct relationship between time, speed, and distance. Option B is also incorrect because it does not represent the correct relationship between time, speed, and distance. Option C is the correct equation because it represents the relationship between time, speed, and distance.

Conclusion

Frequently Asked Questions

What is the relationship between time, speed, and distance? The relationship between time, speed, and distance is given by the formula d = rt, where d is the distance, r is the speed, and t is the time.
How can we use the formula d = rt to model the situation of a giraffe running at a rate of 32 miles per hour? We can substitute the given values into the formula d = rt to get d = 32t.
What is the correct equation that models the situation of a giraffe running at a rate of 32 miles per hour? The correct equation is d = 32t.

Additional Resources

Khan Academy: Speed and Velocity
Mathway: Distance, Speed, and Time
Wolfram Alpha: Distance, Speed, and Time

Discussion

What other situations can we use the formula d = rt to model?
How can we use the formula d = rt to solve real-world problems?
What are some common mistakes to avoid when using the formula d = rt?

Final Thoughts

In conclusion, the equation that models the situation of a giraffe running at a rate of 32 miles per hour is d = 32t. This equation represents the relationship between time, speed, and distance, and it can be used to determine the distance covered by the giraffe in a given time. We hope that this article has provided a clear understanding of the concept of speed and the relationship between time, speed, and distance.

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions related to the concept of speed and the relationship between time, speed, and distance.

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

A: The relationship between time, speed, and distance is given by the formula d = rt, where d is the distance, r is the speed, and t is the time.

Q: How can we use the formula d = rt to model the situation of a giraffe running at a rate of 32 miles per hour?

A: We can substitute the given values into the formula d = rt to get d = 32t.

Q: What is the correct equation that models the situation of a giraffe running at a rate of 32 miles per hour?

A: The correct equation is d = 32t.

Q: What other situations can we use the formula d = rt to model?

A: We can use the formula d = rt to model any situation where we know the speed and time, and we want to find the distance. For example, we can use it to model the situation of a car driving at a speed of 60 miles per hour for 2 hours.

Q: How can we use the formula d = rt to solve real-world problems?

A: We can use the formula d = rt to solve real-world problems such as calculating the distance traveled by a car, the distance covered by a runner, or the distance between two cities.

Q: What are some common mistakes to avoid when using the formula d = rt?

A: Some common mistakes to avoid when using the formula d = rt include:

Not converting units correctly (e.g. miles per hour to kilometers per hour)
Not using the correct formula (e.g. using d = rt instead of d = rt/2)
Not checking the units of the variables (e.g. making sure that the units of distance and speed are consistent)

Q: Can we use the formula d = rt to model situations where the speed is not constant?

A: No, the formula d = rt assumes that the speed is constant. If the speed is not constant, we need to use a different formula, such as the equation of motion.

Q: Can we use the formula d = rt to model situations where the time is not given?

A: No, the formula d = rt requires that we know the time. If the time is not given, we need to use a different formula, such as the equation of motion.

Q: Can we use the formula d = rt to model situations where the distance is not given?

A: Yes, we can use the formula d = rt to model situations where the distance is not given. We can rearrange the formula to solve for the distance.

Additional Resources

Khan Academy: Speed and Velocity
Mathway: Distance, Speed, and Time
Wolfram Alpha: Distance, Speed, and Time

Discussion

What other situations can we use the formula d = rt to model?
How can we use the formula d = rt to solve real-world problems?
What are some common mistakes to avoid when using the formula d = rt?

Final Thoughts

In conclusion, the formula d = rt is a powerful tool that can be used to model a wide range of situations. By understanding the relationship between time, speed, and distance, we can use this formula to solve real-world problems and make informed decisions. We hope that this article has provided a clear understanding of the concept of speed and the relationship between time, speed, and distance.