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According to a map of Arkansas, a number of good roads connect some of the towns south of Little Rock. The road between Malvern and Benton is 23 miles long, and between Benton and Pine Bluff is 62 miles long. The road between Malvern and Sheridan is 28 miles long, and then from Sheridan to Pine Bluff is 22 miles long. Arkadelphia is connected to two towns: it is 12 miles from Gurden and 21 miles from Sheridan. Fordyce has three roads to these towns: 45 miles to Pine Bluff, 39 miles to Sheridan, and 27 miles to Camden. The road from Gurden to Camden is 38 miles.

Unfortunately, the road from Fordyce to Sheridan is closed due to dangerous road conditions caused by the recent bad weather. Find the shortest route between each pair of towns:

a. Malvern and Pine Bluff
b. Camden and Pine Bluff
c. Benton and Arkadelphia
d. Fordyce and Malvern

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

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