We know that Bill covers \(120\) feet at \(3\) feet per sec.
Thus, the time taken to cover the walkway will be \(\frac{120}{3} \to 40\) seconds.
Since his default walking speed is \(6, \) then the amount he can cover in \(40\) seconds is \(6 \cdot 40 \to240.\)
Now he has \(60\) feet left to cover, which will take him \(\frac{60}{3} \to 20\) seconds.
Since the Average speed=The Total distance/TheTotal time, we get \(\frac{300}{20+40} \to \frac{300}{60}=\boxed{5}\) feet per second is his average rate.