Question

using the paths shown, how long is the shortest route from milford to georgetown?
arcadia 3.9 km to milford, milford 8.1 km to oak grove, oak grove 12.3 km to georgetown and 7.8 km to newberry, newberry 5.5 km to georgetown.
blank km
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Explanation:

Step1: Identify possible routes from Milford to Georgetown.

First, the route Milford -> Oak Grove -> Georgetown: length is \(8.1 + 12.3\). Second, the route Milford -> Oak Grove -> Newberry -> Georgetown: length is \(8.1 + 7.8 + 5.5\). We need to calculate both and find the shorter one.

Step2: Calculate the first route's length.

\(8.1 + 12.3 = 20.4\) km.

Step3: Calculate the second route's length.

First, \(8.1 + 7.8 = 15.9\) km. Then, \(15.9 + 5.5 = 21.4\) km? Wait, no, wait. Wait, Milford to Oak Grove is 8.1, Oak Grove to Newberry is 7.8, Newberry to Georgetown is 5.5. Wait, but also, is there a route from Milford to Arcadia? No, the question is from Milford to Georgetown. Wait, maybe I misread. Wait, the nodes: Milford is connected to Arcadia (3.9 km) and Oak Grove (8.1 km). But we need from Milford to Georgetown. So possible paths:

1. Milford -> Oak Grove -> Georgetown: \(8.1 + 12.3 = 20.4\) km.

1. Milford -> Oak Grove -> Newberry -> Georgetown: \(8.1 + 7.8 + 5.5\). Let's calculate that: \(8.1 + 7.8 = 15.9\), \(15.9 + 5.5 = 21.4\) km. Wait, but 20.4 is less than 21.4? Wait, no, wait, maybe I made a mistake. Wait, is there a shorter path? Wait, no, the other path: Milford to Arcadia is 3.9, but Arcadia to where? The diagram shows Arcadia -> Milford (3.9), Milford -> Oak Grove (8.1), Oak Grove -> Georgetown (12.3) or Oak Grove -> Newberry (7.8) -> Georgetown (5.5). So the two possible paths from Milford to Georgetown are:

Path 1: Milford - Oak Grove - Georgetown: \(8.1 + 12.3 = 20.4\) km.

Path 2: Milford - Oak Grove - Newberry - Georgetown: \(8.1 + 7.8 + 5.5 = 21.4\) km.

Wait, but 20.4 is shorter? Wait, but wait, maybe I miscalculated. Wait, 8.1 + 12.3: 8 + 12 = 20, 0.1 + 0.3 = 0.4, so 20.4. Then 8.1 + 7.8: 8 + 7 = 15, 0.1 + 0.8 = 0.9, so 15.9. Then 15.9 + 5.5: 15 + 5 = 20, 0.9 + 0.5 = 1.4, so 21.4. So 20.4 is shorter? Wait, but that seems odd. Wait, maybe the path is Milford to Oak Grove (8.1) then Oak Grove to Georgetown (12.3) is 20.4, or Milford to Oak Grove (8.1) to Newberry (7.8) to Georgetown (5.5) is 21.4. So the shortest is 20.4? Wait, but wait, maybe I missed a path. Wait, no, the diagram shows Milford connected to Arcadia (3.9) and Oak Grove (8.1). Arcadia is not connected to Oak Grove or Georgetown, so the only paths from Milford are through Oak Grove. So the two paths are the two mentioned. So the shortest is 20.4? Wait, but let me check again.

Wait, 8.1 (Milford to Oak Grove) + 12.3 (Oak Grove to Georgetown) = 20.4.

8.1 + 7.8 + 5.5 = 21.4. So 20.4 is shorter. So the shortest route is 20.4 km.

Wait, but maybe I made a mistake. Wait, the problem says "using the paths shown". Let me re-express the distances:

• Milford to Oak Grove: 8.1 km

• Oak Grove to Georgetown: 12.3 km

• Oak Grove to Newberry: 7.8 km

• Newberry to Georgetown: 5.5 km

• Arcadia to Milford: 3.9 km (but Arcadia is not connected to Georgetown or Oak Grove, so that path is a dead end for going to Georgetown)

So the possible routes from Milford to Georgetown are:

1. Milford -> Oak Grove -> Georgetown: 8.1 + 12.3 = 20.4 km

1. Milford -> Oak Grove -> Newberry -> Georgetown: 8.1 + 7.8 + 5.5 = 21.4 km

Since 20.4 < 21.4, the shortest route is 20.4 km.

Answer:

20.4