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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.