Route Distance 541707

1. **State the problem:** We need to find a route visiting Bank, Post Office, and Dry Cleaners starting and ending at Home, with total distance less than $12.5$ miles. 2. **Given distances:** - Home to Bank = $2.5$ miles - Home to Post Office = $2$ miles - Home to Dry Cleaners = $4$ miles - Bank to Post Office = $2$ miles - Bank to Dry Cleaners = $3.5$ miles - Post Office to Dry Cleaners = $5$ miles 3. **Calculate total distances for each route:** **A. Home, Bank, Post Office, Dry Cleaners, Home** $$2.5 + 2 + 5 + 4 = 13.5$$ miles **B. Home, Post Office, Dry Cleaners, Bank, Home** $$2 + 5 + 3.5 + 2.5 = 13$$ miles **C. Home, Dry Cleaners, Post Office, Bank, Home** $$4 + 5 + 2 + 2.5 = 13.5$$ miles **D. Home, Bank, Dry Cleaners, Post Office, Home** $$2.5 + 3.5 + 5 + 2 = 13$$ miles **E. Home, Post Office, Bank, Dry Cleaners, Home** $$2 + 2 + 3.5 + 4 = 11.5$$ miles 4. **Check which total is less than $12.5$ miles:** Only route E has total distance $$11.5 < 12.5$$ miles. 5. **Conclusion:** The route that satisfies the condition is **E. Home, Post Office, Bank, Dry Cleaners, Home**. **Final answer:** Route E with total distance $11.5$ miles.