Let's denote the average rate of the ferry as \( r \) (in miles per hour).
From City A to City B, the distance is 93 miles. The time taken to travel this distance can be expressed as:
\[ \text{Time from A to B} = \frac{93}{r} \]
From City B to City C, the distance is 62 miles. The time taken to travel this distance can be expressed as:
\[ \text{Time from B to C} = \frac{62}{r} \]
According to the problem, the time from City B to City C takes 2 hours less than the time from City A to City B. Therefore, we can write the equation:
\[ \frac{62}{r} = \frac{93}{r} - 2 \]
Now, we can eliminate the fractions by multiplying through by \( r \):
\[ 62 = 93 - 2r \]
Next, we can solve for \( r \):
\[ 2r = 93 - 62 \] \[ 2r = 31 \] \[ r = \frac{31}{2} \] \[ r = 15.5 \]
Thus, the average rate of the ferry is \( 15.5 \) miles per hour.