U.S. Interstate 64 runs between Portsmouth, VA, at I-264 on the eastern end to St. Louis, MO, at I-270 on the western end. While passing through six states and five more major cities, I-64 intersects nine more interstate highways. The number of miles in each state is as follows.
Missouri--14 miles, Illinois--132 miles, Indiana--124 miles, Kentucky--196 miles, West Virginia--187 miles, Virginia--298 miles.
(a) Find the mean distance between major cities along I-64. (Give your answer correct to the nearest mile.)
. miles
(b) Find the mean distance between interchanges with interstate highways along I-64. (Give your answer correct to the nearest mile.)
156
To find the mean distance between major cities along Interstate 64 (I-64), we need to divide the total distance traveled by the number of major cities it passes through.
According to the given information, I-64 passes through five major cities: Portsmouth, VA; Richmond, VA; Lexington, KY; Louisville, KY; and St. Louis, MO.
The total distance traveled along I-64 is the sum of the distances in each state it passes through:
Virginia: 298 miles
West Virginia: 187 miles
Kentucky: 196 miles
Therefore, the total distance traveled is 298 + 187 + 196 = 681 miles.
To find the mean distance between major cities, we divide the total distance traveled by the number of major cities:
Mean distance between major cities = Total distance traveled / Number of major cities
Mean distance between major cities = 681 miles / 5 major cities
Mean distance between major cities ≈ 136 miles
So, the mean distance between major cities along I-64 is approximately 136 miles.
To find the mean distance between interchanges with interstate highways along I-64, we divide the total distance traveled by the number of interchanges.
According to the given information, I-64 intersects nine other interstate highways.
Mean distance between interchanges = Total distance traveled / Number of interchanges
Mean distance between interchanges = 681 miles / 9 interchanges
Mean distance between interchanges ≈ 75.7 miles
So, the mean distance between interchanges with interstate highways along I-64 is approximately 75.7 miles.