To save on gasoline expenses, Edith and Mathew agreed to carpool together for traveling to and from work. Edith preferred to travel on I-20 highway as it was usually the fastest, taking 25 minutes in the absence of traffic delays. Mathew pointed out that traffic jams on the highway can lead to long delays making the trip 45 minutes. He preferred to travel along Shea Boulevard, which was longer (35 minutes), but rarely had traffic jams. Edith agreed that in case of traffic jams, Shea Boulevard was a reasonable alternative. Neither of them knows the state of the highway ahead of time

It's an interesting scenario -- but what is the question?

To determine which route Edith and Mathew should take for their carpool, we need to consider the time it takes on both the I-20 highway and Shea Boulevard, as well as the likelihood of traffic delays.

For the I-20 highway:
- The usual travel time without traffic is 25 minutes.
- However, if there is a traffic jam, the travel time can increase to 45 minutes.

For Shea Boulevard:
- The travel time on Shea Boulevard is longer at 35 minutes.
- However, traffic jams on Shea Boulevard are rare.

Since neither Edith nor Mathew knows the state of the highway ahead of time, one approach to decide the most advantageous route is to consider the expected travel times for both routes.

Let's calculate the expected travel times for each route:

Expected travel time for I-20:
Assuming equal chances of encountering traffic or no traffic, we can take the average of the two possible travel times:
(25 minutes + 45 minutes) / 2 = 35 minutes (expected travel time for I-20)

Expected travel time for Shea Boulevard:
Since traffic jams on Shea Boulevard are rare, we can assume a lower chance of encountering traffic delays compared to I-20.
We'll consider a 10% chance of encountering traffic, leading to a delay of 10 minutes.
Thus, the expected travel time on Shea Boulevard would be:
(35 minutes + (10% * 10 minutes)) = 36 minutes (expected travel time for Shea Boulevard)

Comparing the expected travel times, we find that the expected travel time for I-20 is 35 minutes, while the expected travel time for Shea Boulevard is 36 minutes.

Based on these calculations, it seems that on average, Edith and Mathew would save one minute by taking the I-20 highway, even considering the possibility of traffic delays. Therefore, they could choose the I-20 highway as their primary route, with Shea Boulevard serving as an alternative in case of traffic jams.