#### Answer

Using the Brute Force Method, we can see that the shortest route to run errands and return home is 15 miles.

#### Work Step by Step

If we start and end at home, there are 6 possible routes we can take. We can find the total weight of each route.
The route is Home, Bank, Post Office, Market, Home.
total weight = 3 + 4 + 4.5 + 3.5 = 15
The distance of this route is 15 miles.
The route is Home, Bank, Market, Post Office, Home.
total weight = 3 + 5 + 4.5 + 5.5 = 18
The distance of this route is 18 miles.
The route is Home, Market, Post Office, Bank, Home.
total weight = 3.5 + 4.5 + 4 + 3 = 15
The distance of this route is 15 miles.
The route is Home, Market, Bank, Post Office, Home.
total weight = 3.5 + 5 + 4 + 5.5 = 18
The distance of this route is 18 miles.
The route is Home, Post Office, Market, Bank, Home.
total weight = 5.5 + 4.5 + 5 + 3 = 18
The distance of this route is 18 miles.
The route is Home, Post Office, Bank, Market, Home.
total weight = 5.5 + 4 + 5 + 3.5 = 18
The distance of this route is 18 miles.
Using the Brute Force Method, we can see that the shortest route to run errands and return home is 15 miles.