A few months ago, I was going from Bangalore to Thiruvannamalai. While most of the roads in Tamilnadu are good, NH-66 connecting Krishnagiri and Thiruvannamalai has parts which are good, and other parts are muddy and often pass through populated areas.
In such a situation, the intuition is often to drive very fast on the good part of the road, faster than what you would have done if the whole road were good. The intuition is to "make up" for the slow speed in the bad part of the road. In the slow portion, we are bottlenecked by congestion on the road, so we cannot do much. In the fast portion, we can be more aggressive and drive faster.
Let us say total distance to be travelled is 400km, of which 200km is good and 200km is bad. Speed on good road is 100km/hr and speed on bad road is 20km/hr. What do you think is the average speed during the journey. First intuition is that the average speed should be (100 + 20) / 2 = 60km/hr.
However, actually, the average speed is the harmonic mean of 100 and 20.
Time taken to cover fast part: 200 / 100 = 2 hrs
Time taken to cover slow part: 200 / 20 = 10 hrs
Total time: 12 hrs
Average speed: 400/12 km/hr = 33.3 km/hr = 2 * 100 * 20 / (100 + 20) km/hr.
Let's see how much does speeding buy us. We decide to drive at 20% higher speed in the fast portion, at 120 km/hr. Then average speed for the journey would be 2 * 120 * 20 / (120 + 20) = 34.3 km/hr, a mere 3% speedup over 33.3km/hr.
If similar 20% speedup could be had for the slower part from 20km/hr to 24km/hr, gain would be much more handsome. Average speed up goes up to 2 * 100 * 24 / (100 + 24) = 38.7km/hr, which is a handsome 16% speedup!
Reason is that most of the time is spent on the slow road, so it makes sense to increase the speed there. Not doing so is falling prey to Streetlight effect
Moral of the story is that it makes more sense to make modest speedups in slower portion of the job rather than big speedups in faster portion. And speeding on the road is not worth the risk.