A Freight Train Is Traveling At An Average Rate Of 45 Miles Per Hour. Which Equation Represents The Situation?Let $h$ Represent The Hours Traveled. Let $m$ Represent The Miles Traveled.$\begin{array}{l} M = 45h \\ H = 45m \\ M =

Introduction

In physics and mathematics, the relationship between speed, time, and distance is a fundamental concept that is often represented by a simple equation. In this article, we will explore the equation that represents the situation of a freight train traveling at an average rate of 45 miles per hour.

The Equation

Let's start by defining the variables:

• $h$ represents the hours traveled
• $m$ represents the miles traveled

The equation that represents the situation is:

$$m = 45h$$

Explanation

This equation states that the distance traveled ($m$) is equal to the speed of the train (45 miles per hour) multiplied by the time traveled ($h$). In other words, if the train travels for $h$ hours, it will cover a distance of $m$ miles.

Why This Equation?

This equation is a direct application of the formula:

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

In this case, the speed is 45 miles per hour, and the time is $h$ hours. Therefore, the distance traveled is equal to the speed multiplied by the time.

Alternative Equations

Some readers may be wondering why the equation is not:

$$h = 45m$$

or

$$m = 45h^{-1}$$

The reason is that the first equation is not a correct representation of the situation. The second equation is also not correct, as it implies that the time traveled is inversely proportional to the distance traveled, which is not the case.

Conclusion

In conclusion, the equation that represents the situation of a freight train traveling at an average rate of 45 miles per hour is:

$$m = 45h$$

This equation is a direct application of the formula:

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

Example Problems

Here are a few example problems to illustrate the use of this equation:

• If the freight train travels for 2 hours, how many miles will it cover?
• If the freight train covers a distance of 90 miles, how many hours will it take to travel that distance?

Solution to Example Problems

• If the freight train travels for 2 hours, the distance traveled will be:

$$m = 45h$$

$$m = 45 \times 2$$

$$m = 90$$

Therefore, the freight train will cover a distance of 90 miles in 2 hours.

• If the freight train covers a distance of 90 miles, the time taken will be:

$$m = 45h$$

$$90 = 45h$$

$$h = 2$$

Therefore, the freight train will take 2 hours to cover a distance of 90 miles.

Real-World Applications

The equation $m = 45h$ has many real-world applications, including:

• Calculating the distance traveled by a vehicle
• Determining the time taken to travel a certain distance
• Planning routes for transportation

Conclusion

In conclusion, the equation $m = 45h$ represents the situation of a freight train traveling at an average rate of 45 miles per hour. This equation is a direct application of the formula:

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

$$

Q: What is the equation $m = 45h$ used for?

A: The equation $m = 45h$ is used to calculate the distance traveled by a vehicle, given its speed and time traveled. It is a direct application of the formula:

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

Q: What are the variables in the equation $m = 45h$?

A: The variables in the equation $m = 45h$ are:

• $h$: the hours traveled
• $m$: the miles traveled

Q: What is the speed in the equation $m = 45h$?

A: The speed in the equation $m = 45h$ is 45 miles per hour.

Q: Can I use the equation $m = 45h$ for any speed?

A: No, the equation $m = 45h$ is specific to a speed of 45 miles per hour. If you want to calculate the distance traveled for a different speed, you will need to use a different equation.

Q: How do I use the equation $m = 45h$ to calculate the distance traveled?

A: To use the equation $m = 45h$ to calculate the distance traveled, simply plug in the values for $h$ and $m$. For example, if the freight train travels for 2 hours, the distance traveled will be:

$$m = 45h$$

$$m = 45 \times 2$$

$$m = 90$$

Therefore, the freight train will cover a distance of 90 miles in 2 hours.

Q: Can I use the equation $m = 45h$ to calculate the time taken to travel a certain distance?

A: Yes, you can use the equation $m = 45h$ to calculate the time taken to travel a certain distance. To do this, simply rearrange the equation to solve for $h$:

$$h = \frac{m}{45}$$

For example, if the freight train covers a distance of 90 miles, the time taken will be:

$$h = \frac{m}{45}$$

$$h = \frac{90}{45}$$

$$h = 2$$

Therefore, the freight train will take 2 hours to cover a distance of 90 miles.

Q: What are some real-world applications of the equation $m = 45h$?

A: Some real-world applications of the equation $m = 45h$ include:

• Calculating the distance traveled by a vehicle
• Determining the time taken to travel a certain distance
• Planning routes for transportation
• Estimating the fuel consumption of a vehicle
• Calculating the cost of transportation

Q: Can I use the equation $m = 45h$ for other types of transportation?

A: Yes, the equation $m = 45h$ can be used for other types of transportation, such as airplanes, boats, and bicycles. Simply plug in the speed and time values for the specific type of transportation.

Q: What are some common mistakes to avoid when using the equation $m = 45h$?

A: Some common mistakes to avoid when using the equation $m = 45h$ include:

• Using the wrong units (e.g. miles per hour instead of kilometers per hour)
• Forgetting to plug in the correct values for $h$ and $m$
• Not checking the units of the answer
• Not considering the limitations of the equation (e.g. it assumes a constant speed)

Conclusion

In conclusion, the equation $m = 45h$ is a simple and powerful tool for calculating the distance traveled by a vehicle, given its speed and time traveled. By understanding the variables and limitations of the equation, you can use it to solve a wide range of problems in physics, engineering, and everyday life.