(2) Joseph runs marathons at a constant rate of 5 miles per hour. \begin{tabular}{l|l} (a) Write an equation that & (b) Explain what each part of the equation represents in the \ represents this situation. & situation. \ $$ y=5 $$ & \end{tabular}

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To solve this problem, we need to create an equation that represents Joseph's running situation and then explain the components of that equation.

### Step 1: Write the Equation

Joseph runs at a constant rate of 5 miles per hour. We can express the relationship between distance, rate, and time using the formula:

$$
d = rt
$$

Where:
- $$ d $$ is the distance (in miles),
- $$ r $$ is the rate (in miles per hour),
- $$ t $$ is the time (in hours).

Since Joseph runs at a constant rate of 5 miles per hour, we can substitute $$ r $$ with 5:

$$
d = 5t
$$

### Step 2: Explain Each Part of the Equation

Now, let's explain what each part of the equation $$ d = 5t $$ represents:

- **$$ d $$**: This variable represents the total distance that Joseph runs in miles. It is the output of the equation, depending on how long he runs.

- **5**: This is the constant rate at which Joseph runs, measured in miles per hour. It indicates that for every hour he runs, he covers 5 miles.

- **$$ t $$**: This variable represents the time in hours that Joseph spends running. It is the input of the equation, determining how far he will run based on the duration of his run.

### Summary

The equation $$ d = 5t $$ effectively models the relationship between the distance Joseph runs, the rate at which he runs, and the time he runs. Each component of the equation plays a crucial role in understanding how far he can run based on his speed and the time he dedicates to running.
The equation is $$ d = 5t $$, where: - $$ d $$ is the distance in miles, - 5 is the running rate of 5 miles per hour, - $$ t $$ is the time in hours. This equation shows that the distance Joseph runs is equal to his running rate multiplied by the time he spends running.

(2) Joseph runs marathons at a constant rate of 5 miles per hour. \begin{tabular}{l|l} (a) Write an equation that & (b) Explain what each part of the equation represents in the \\ represents this situation. & situation. \\ \( y=5 \) & \end{tabular}

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