1. **State the problem:** We need to find the shortest possible route from Brighton to Cheltenham using the given distances between towns. 2. **List the towns and distances:** - Derby to Lincoln: 56 - Derby to Northampton: 66 - Derby to Cheltenham: 97 - Northampton to Lincoln: 92 - Northampton to Cheltenham: 69 - Northampton to London: 67 - London to Brighton: 53 - Brighton to Bournemouth: 98 - Bournemouth to Cheltenham: 119 - London to Bournemouth: 108 3. **Identify possible routes from Brighton to Cheltenham:** - Route A: Brighton → London → Northampton → Cheltenham - Route B: Brighton → London → Bournemouth → Cheltenham - Route C: Brighton → Bournemouth → Cheltenham - Route D: Brighton → London → Northampton → Derby → Cheltenham - Route E: Brighton → London → Northampton → Derby → Lincoln → Northampton → Cheltenham (longer, so ignore) 4. **Calculate distances for each route:** - Route A: Brighton to London = 53, London to Northampton = 67, Northampton to Cheltenham = 69 Total = $53 + 67 + 69 = 189$ - Route B: Brighton to London = 53, London to Bournemouth = 108, Bournemouth to Cheltenham = 119 Total = $53 + 108 + 119 = 280$ - Route C: Brighton to Bournemouth = 98, Bournemouth to Cheltenham = 119 Total = $98 + 119 = 217$ - Route D: Brighton to London = 53, London to Northampton = 67, Northampton to Derby = 66, Derby to Cheltenham = 97 Total = $53 + 67 + 66 + 97 = 283$ 5. **Compare totals:** - Route A: 189 miles - Route B: 280 miles - Route C: 217 miles - Route D: 283 miles 6. **Conclusion:** The shortest route is Route A with a total distance of $189$ miles. **Final answer:** The shortest possible route from Brighton to Cheltenham is via London and Northampton with a length of **189 miles**.