Exercise
Suppose you have a 65-mile drive. Assume you travel the entire distance at a constant 65 mph, with no stops. How long does the trip take?
On a second trip, you travel the first 52 miles at 65 mph, but congestion reduces your average speed over the final 13 miles to 26 mph. How long does the whole trip take?
On a third trip, you travel the first 52 miles at 75 mph, exceeding the assumed 65 mph speed limit. You still average 26 mph over the final 13 miles. For this comparison, hold the congestion unchanged even though you reach it at a different time. How long does the trip take, and how much time does the higher speed save?
Facts
At a constant 65 mph, the 65-mile trip takes 65/65 = 1 hour.
With congestion, the first 52 miles take 52/65 = 0.8 hour, or 48 minutes. The final 13 miles take 13/26 = 0.5 hour, or 30 minutes. The total is 78 minutes: 1 hour and 18 minutes.
At 75 mph for the first leg, those 52 miles take 41 minutes and 36 seconds. Adding the same 30-minute final segment gives a total of 1 hour, 11 minutes, and 36 seconds. The time saved is 6 minutes and 24 seconds.
Without congestion, the final 13 miles would take 12 minutes at 65 mph. Spending 30 minutes on that segment therefore adds 18 minutes to the trip.
Thoughts and Opinions
Where do you draw the line?
In New Jersey, where I am from, a drive down the shore can put this question in familiar surroundings. The open highway gives way to a slower final stretch, and the minutes may feel different depending on where we spend them.
Imagine hearing a traffic report: “Expect half-hour delays.” A delay normally means extra travel time compared with some expected or usual trip. That is different from spending half an hour in congestion.
In our example, the slow segment takes 30 minutes, but it would already have taken 12 minutes without the slowdown. We can describe it accurately as 30 minutes in the slow segment or 18 additional minutes. Those descriptions answer different questions. A report of a 30-minute delay would need its own baseline; our calculation does not establish that the report means only 18 minutes.
The same care applies to the time saved by the faster first leg. In this example it is 6 minutes and 24 seconds. Leaving that much earlier would produce the same arrival time if the travel conditions stayed unchanged. In a real trip, changing the departure or arrival time can also change the traffic encountered.
Numbers can help us compare choices, but first we need to know what each number measures. Does it describe the whole trip, one part of it, or the difference between two trips? What assumptions stay fixed while we compare?
Ultimately numbers cannot do the thinking for us. What would you want to know before deciding what those six minutes and twenty-four seconds are worth?
Feel free to email me with your thoughts and opinions on this matter at [email protected].