📍 Scene Setup
Josh is deep in the outback on a camping trip when his GPS dies mid-navigation. He pulls out an old paper road map. The campsite is marked as point F, but the map shows multiple possible routes with different distances.
It's getting dark. Josh needs to figure out the fastest routes before he runs out of daylight. Six navigation problems stand between him and a warm campfire.
🗺️ Road Map, Distances in Kilometres
A = starting point · F = campsite · Numbers = distance in km between locations
1
Route 1, Northern Road
Josh reads off the northern route on the map: A → B → D → F.
What is the total distance of this route in km?
Add up the distances along each road segment.
💡 A, B = 2, B, D = 5, D, F = 3. Add them all together.
✅ Route A, B, D, F = 2+5+3 = 10 km. Long way round, let's check the other routes.
2
Route 2, Cut Through
The second route cuts diagonally: A → B → E → F.
What is the total distance of this route?
A, B, then B cuts diagonally down to E, then E, F.
💡 A, B = 2, B, E = 4, E, F = 1. Add them.
✅ Route A, B, E, F = 2+4+1 = 7 km. Better, but there might be something even shorter.
3
Route 3, Southern Road
The southern route stays lower: A → C → E → F.
What is the total distance of this route?
A drops down to C, across to E, then the short E, F leg.
💡 A, C = 2, C, E = 3, E, F = 1. Add them.
✅ Route A, C, E, F = 2+3+1 = 6 km. That's the best yet!
4
Campsite, Shortest Route to F
Josh has now checked all three main routes to the campsite (F).
What is the shortest distance from A to F?
Compare your answers from routes 1, 2, and 3 and pick the minimum.
💡 Route 1 = 10, Route 2 = 7, Route 3 = 6. What is the minimum?
✅ 6 km via A, C, E, F. Shortest path confirmed, southern route wins!
5
Water Stop, Shortest Route to E
Josh needs to stop at the water tank at location E before reaching the campsite. What is the shortest distance from A to E?
Find all paths from A to E and pick the shortest.
💡 Two paths to E: A, B, E = 2+4 = 6, or A, C, E = 2+3 = 5. Which is shorter?
✅ 5 km via A, C, E. The southern route to the water stop is also faster!
6
Turnoff, Shortest Route to D
There's a lookout at location D. What is the shortest distance from A to D?
Check the map for all paths between A and D.
💡 The only direct route to D goes via B: A, B, D = 2+5 = 7. There's no shorter path.
✅ 7 km via A, B, D. That's the only route to the lookout, navigation complete!
🏕️
Made It to Camp!
Josh found the campsite in record time, 6 km via the southern route A, C, E, F. Every route verified, every distance checked. The GPS can stay dead; this worked out better anyway.