To express the relationship between the number of hours driven \( h \) and the total amount of miles driven \( m \), we can use the formula for distance:
\[ m = r \cdot h \]
where \( r \) is the rate of speed. In this case, the family's driving speed is 55 miles per hour, so we can substitute \( r \) with 55:
\[ m = 55h \]
To find out how far they drove after 4 hours, we can substitute \( h \) with 4 in the equation:
\[ m = 55 \cdot 4 \] \[ m = 220 \]
So, the family drove 220 miles after 4 hours.