Answer :
Final answer:
The shortest routes are Malvern to Pine Bluff through Sheridan (85 miles), Camden to Pine Bluff through Fordyce (93 miles), Benton to Arkadelphia through Malvern, Sheridan, and Arkadelphia (73 miles), and Fordyce to Malvern through Camden, Gurden, Arkadelphia, and Sheridan (105 miles).
Explanation:
Let's find the shortest routes between the given pairs of towns:
a. Malvern and Pine Bluff:
- Malvern to Benton: 23 miles
- Benton to Pine Bluff: 62 miles
- Total distance: 23 + 62 = 85 miles
b. Camden and Pine Bluff:
- Camden to Gurden: 38 miles
- Gurden to Arkadelphia: 12 miles
- Arkadelphia to Sheridan: 21 miles
- Sheridan to Pine Bluff: 22 miles
- Total distance: 38 + 12 + 21 + 22 = 93 miles
c. Benton and Arkadelphia:
- Benton to Malvern: 23 miles
- Malvern to Sheridan: 28 miles
- Sheridan to Arkadelphia: 22 miles
- Total distance: 23 + 28 + 22 = 73 miles
d. Fordyce and Malvern:
Since the road from Fordyce to Sheridan is closed, we need to find an alternative route.
- Fordyce to Camden: 27 miles
- Camden to Gurden: 38 miles
- Gurden to Arkadelphia: 12 miles
- Arkadelphia to Malvern: 28 miles
Total distance: 27 + 38 + 12 + 28 = 105 miles
Therefore, the shortest routes are:
a. Malvern to Pine Bluff: 85 miles
b. Camden to Pine Bluff: 93 miles
c. Benton to Arkadelphia: 73 miles
d. Fordyce to Malvern: 105 miles