The given equation that represents the relationship between the number of inches a candle has burned away (\(b\)) and time in hours (\(t\)) is:
\[ b = 1.5t \]
In this equation, the coefficient of \(t\) (which is 1.5) represents the rate at which the candle burns. Specifically, it indicates that the candle burns 1.5 inches for every hour that passes.
Thus, the rate at which the candle burns is 1.5 inches per hour.