Two buses start at the same point and travel in opposite directions. The first bus travels 10 miles per hour faster than the second bus. In 3 hours, the buses are 282 miles apart. Use the formula below to determine the rate of the second bus.

To find the rate of the second bus, we can solve the equation that has been given:

\[ 3(r + 10) + 3r = 282 \]

This equation represents the distance traveled by both buses in 3 hours. The first bus travels at a speed of \( r + 10 \) (10 mph faster than the second bus), and the second bus travels at a speed of \( r \).

Let's simplify the equation:

1. Distribute the 3:
\[
3(r + 10) + 3r = 282
\]
becomes
\[
3r + 30 + 3r = 282
\]

2. Combine like terms:
\[
6r + 30 = 282
\]

3. Subtract 30 from both sides:
\[
6r = 252
\]

4. Divide by 6:
\[
r = 42
\]

Thus, the rate of the second bus is \( \boxed{42} \) mph.