Project description
Georges Thanksgiving Trip
George is invited by his sister, Dorothy, to attend a family reunion during the Thanksgiving weekend. Dorothy lives in Denver, NY, about 90 miles northeast of New York City. George lives in Washington, DC, about 215 miles south of New York City. George decides to visit Dorothy and to travel to her place by car.
The only problem is that road traffic during the Thanksgiving holidays is terrible along the East Coast of the United States. George would normally travel to Dorothys house by taking Interstate Highway 95. This is the major link connecting Washington and New York City. However, during Thanksgiving, the traffic on I-95 is usually bad, leading to major delays.
George decides to explore an alternate route to traveling to Dorothys. This route would be a few miles longer. Also, he would encounter a 60 mile segment of road in a rural area, and he would have to travel slowly on this segment. The good feature about the alternate route is that it is unlikely to suffer from Thanksgiving traffic.
A map showing the two routes to Dorothys house is offered in Figure 1.
Based on his experience in traveling along I-95 during Thanksgiving holidays, George has developed a good sense of the likelihood of delays that he can encounter on the journey. Table 1 shows the probability distributions he has created for all the segments of his trip to Dorothy for both the I-95 route and the alternate route.
Assignment
Using the information supplied in Figure 1 and Table 1, determine the expected amount of time it will take George to travel from Washington, DC to his sisters house, employing both the I-95 and alternate route. SHOW YOUR WORK, DEMONSRATING HOW YOU ARRIVED AT THE ANSWERS YOU PROVIDE.
Two routes to George sister\’s house:
Figure 1
Route 1:
George sister house upstate New York to Kingston 10 miles using Rural Road; Kingston to New York City 80 miles using highway; New York City to Baltimore 175 miles using highway ; Baltimore to George house Washington DC 40 miles using highway .
Route 2:
George sister house to East Branch 60 miles using Rural Road; East Branch to Binghamton 50 miles using highway ; Binghamton to Scranton 30 miles using highway ; Scranton to Baltimore 130 miles using highway ; Baltimore to George house 40 miles using highway .
Legend: Highway 70 MPH; Rural 40 MPH
Table 1
Probability Distributions for Travel Times on Journey
Regular Route (East Route)
Probability of achieving schedule, 10%, 20%, 30%, 40% longer than schedule
Segment
Washington-Baltimore 0.70.30.0 0.0 0.0
Baltimore-New York City 0.00.10.2 0.5 0.2
New York City-Kingston 0.10.20.3 0.3 0.1
Kingston-Sister\’s Home 0.80.20.0 0.0 0.0
Alternate Route (West Route)
Probability of achieving schedule, 10%, 20%, 30%, 40% longer than schedule
Segment
Washington-Baltimore0.7 0.30.0 0.0 0.0
Baltimore-Binghamton0.9 0.10.0 0.0 0.0
Binghamton-E Branch0.9 0.10.0 0.0 0.0
E Branch-Sister\’s Home0.8 0.20.0 0.0 0.0
