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.
After driving to work on the I-20 highway for 1 month (20 workdays), they found the highway to be jammed 3 times. Assuming that this month is a good representation of all months ahead, should Edith and Mathew continue to use the highway for traveling to work?
How would you conclusion change for the winter months, if bad weather makes it likely for traffic jams on the highway to increase to 6 days per month?
How would your conclusion change if Mathew purchased a new smart-phone app that could show the status of the highway traffic prior to their drive each morning, thus reducing the probability of them getting into a jam down to only 1day per month (where on this day, the app showed no traffic jam, but a jam developed in the meantime as they were driving along the highway).
To determine if Edith and Mathew should continue using the highway for traveling to work, we need to compare the average travel times for both routes.
First, let's calculate the average travel time on the highway by considering the 20 workdays in the month. The highway gets jammed 3 times, which means there are 20 - 3 = 17 days without traffic delays. On those days, the travel time is 25 minutes. So, the total travel time without delays is 17 * 25 = 425 minutes.
Next, let's find the average travel time on Shea Boulevard. Since there are no traffic jams on this route, the travel time is always 35 minutes per day. Therefore, the total travel time on Shea Boulevard for the 20 workdays is 20 * 35 = 700 minutes.
Comparing the two routes, the total travel time over the month on the highway is 425 minutes and on Shea Boulevard is 700 minutes. Clearly, Shea Boulevard has longer total travel time, so it would not be a better option.
Now, let's consider the scenario for the winter months when bad weather makes traffic jams on the highway increase to 6 days per month. In this case, the number of days without traffic delays on the highway would be 20 - 6 = 14 days. The total travel time without delays is 14 * 25 = 350 minutes. The total travel time on Shea Boulevard remains the same at 700 minutes.
Comparing the two routes, the total travel time over the month on the highway is now 350 minutes and on Shea Boulevard is still 700 minutes. Therefore, even with increased traffic jams in the winter months, the highway still offers a shorter total travel time.
Finally, let's consider the scenario where Mathew purchases a new smart-phone app that shows the status of the highway traffic prior to their drive each morning. This reduces the probability of getting into a jam down to only 1 day per month. This means for 19 days, there are no traffic delays, resulting in a total travel time of 19 * 25 = 475 minutes on the highway. The total travel time on Shea Boulevard remains at 700 minutes.
Comparing the two routes, the total travel time over the month on the highway is now 475 minutes and on Shea Boulevard is still 700 minutes. Therefore, even with the reduced probability of traffic jams, Shea Boulevard still has a longer total travel time.
In conclusion, based on the given information and calculations, Edith and Mathew should continue using the highway for traveling to work as it offers a shorter total travel time compared to Shea Boulevard, regardless of the weather conditions or the availability of a smart-phone app to check traffic status.