To find the constant of proportionality in the equation that relates distance, speed, and time, we can start with the formula for time, which is given by the formula:
\[ t = \frac{d}{r} \]
where \( t \) is the time, \( d \) is the distance, and \( r \) is the speed (or rate).
In this case, Jean drove a total distance of \( d = 448 \) miles at a speed of \( r = 64 \) miles per hour. To calculate the time \( t \), we set up the equation as follows:
\[ t = \frac{448}{64} \]
Now, we can perform the division:
\[ t = 7 \quad \text{hours} \]
In the context of proportionality, we can express this relationship in terms of \( t \) and \( d \). If we isolate \( d \), we have:
\[ d = rt \]
Here, \( r \), the speed, is the constant of proportionality. In this specific example, the constant of proportionality, which is the speed at which Jean is traveling, is:
\[ \text{Constant of proportionality} = 64 \text{ miles per hour.} \]