To find John's rate of speed using the formula \( d = rt \), we can rearrange the formula to solve for \( r \):
\[ r = \frac{d}{t} \]
where:
- \( d \) is the distance (138 miles),
- \( t \) is the time (3 hours).
Now, we can substitute the values into the equation:
\[ r = \frac{138 \text{ miles}}{3 \text{ hours}} = 46 \text{ miles per hour} \]
Therefore, John's rate of speed is 46 miles per hour.