Distances in kilometres (2) - Measuring in Year 5 (age 9-10) by ... - Free Printable

Let me work through each question step by step.

Question 1:
Tommy Turtle is traveling from Moreton-in-Marsh to Bourton-on-the-Water, stopping at Chipping Norton for lunch.

Route: Moreton-in-Marsh → Chipping Norton → Bourton-on-the-Water

- Moreton-in-Marsh to Chipping Norton = 13.5 km
- Chipping Norton to Bourton-on-the-Water = 21 km

Total distance = 13.5 + 21 = 34.5 km

Question 2:
After staying the night in Bourton-on-the-Water, they drive:
Bourton-on-the-Water → Stow-on-the-Wold → Chipping Norton → Moreton-in-Marsh

- Bourton-on-the-Water to Stow-on-the-Wold = 6.5 km
- Stow-on-the-Wold to Chipping Norton = 15 km
- Chipping Norton to Moreton-in-Marsh = 13.5 km

Total distance = 6.5 + 15 + 13.5 = 35 km

Question 3:
If they had returned directly from Bourton-on-the-Water to Moreton-in-Marsh by the shortest route without going shopping.

The shortest route from Bourton-on-the-Water to Moreton-in-Marsh would be:
Bourton-on-the-Water → Stow-on-the-Wold → Moreton-in-Marsh

- Bourton-on-the-Water to Stow-on-the-Wold = 6.5 km
- Stow-on-the-Wold to Moreton-in-Marsh = 7 km

Shortest route = 6.5 + 7 = 13.5 km

In Question 2, they traveled 35 km (going via Chipping Norton).

Difference = 35 - 13.5 = 21.5 km less

Question 4:
What is the shortest distance the bus would have to travel to visit all four towns and return to the start?

This is a "traveling salesman" type problem. We need to find the shortest route that visits all 4 towns and returns to the starting point.

Let me list all the distances:
- Moreton-in-Marsh to Stow-on-the-Wold = 7 km
- Moreton-in-Marsh to Chipping Norton = 13.5 km
- Stow-on-the-Wold to Chipping Norton = 15 km
- Stow-on-the-Wold to Bourton-on-the-Water = 6.5 km
- Chipping Norton to Bourton-on-the-Water = 21 km

There's no direct route shown between Moreton-in-Marsh and Bourton-on-the-Water, so we must go through either Stow-on-the-Wold or Chipping Norton.

Let me try different routes. I'll choose Moreton-in-Marsh as the starting point.

Option 1: Moreton → Stow → Bourton → Chipping → Moreton
= 7 + 6.5 + 21 + 13.5 = 48 km

Option 2: Moreton → Chipping → Bourton → Stow → Moreton
= 13.5 + 21 + 6.5 + 7 = 48 km

Option 3: Moreton → Stow → Chipping → Bourton → (back to Moreton)
To get from Bourton back to Moreton, we'd go through Stow: Bourton → Stow → Moreton
= 7 + 15 + 21 + 6.5 + 7 = 56.5 km (this doesn't make sense as a circuit)

Actually, let me reconsider. For a proper circuit visiting all 4 towns:

Option A: Moreton → Stow → Bourton → Chipping → Moreton
= 7 + 6.5 + 21 + 13.5 = 48 km

Option B: Moreton → Chipping → Bourton → Stow → Moreton
= 13.5 + 21 + 6.5 + 7 = 48 km

Option C: Moreton → Stow → Chipping → Bourton → Stow → Moreton
This revisits Stow, which isn't necessary.

Let me check if there's a better route by trying different starting points:

Starting from Stow-on-the-Wold:
Stow → Moreton → Chipping → Bourton → Stow
= 7 + 13.5 + 21 + 6.5 = 48 km

Stow → Bourton → Chipping → Moreton → Stow
= 6.5 + 21 + 13.5 + 7 = 48 km

Starting from Chipping Norton:
Chipping → Moreton → Stow → Bourton → Chipping
= 13.5 + 7 + 6.5 + 21 = 48 km

Chipping → Bourton → Stow → Moreton → Chipping
= 21 + 6.5 + 7 + 13.5 = 48 km

Starting from Bourton-on-the-Water:
Bourton → Stow → Moreton → Chipping → Bourton
= 6.5 + 7 + 13.5 + 21 = 48 km

Bourton → Chipping → Moreton → Stow → Bourton
= 21 + 13.5 + 7 + 6.5 = 48 km

All these give 48 km. But wait, let me check if there's a shorter path by not using all the edges...

Actually, I realize we MUST use paths that connect all towns. Looking at the diagram, the connections form a network where we can traverse between any two towns.

Let me think about this differently. The minimum spanning tree approach won't work here because we need a circuit (return to start).

For 4 towns, any valid circuit will use exactly 4 edges (one to leave each town and one to enter each town, but since it's a circuit, we count each edge once).

Looking at all possible circuits, they all seem to give 48 km. Let me verify once more:

The key insight: Any circuit visiting all 4 towns must include:
- One edge connecting to/from Moreton
- One edge connecting to/from Stow
- One edge connecting to/from Chipping
- One edge connecting to/from Bourton

But actually, each town appears twice in the circuit (once entered, once exited), so we use 4 edges total.

Hmm, let me reconsider. In a circuit with 4 vertices, we use 4 edges. Let me find the combination that minimizes the total.

Possible edges and their weights:
- M-S: 7
- M-C: 13.5
- S-C: 15
- S-B: 6.5
- C-B: 21

For a valid circuit, we need to select 4 edges that form a cycle through all 4 nodes.

One valid cycle: M-S-B-C-M uses edges: M-S(7), S-B(6.5), B-C(21), C-M(13.5) = 48

Another: M-C-B-S-M uses edges: M-C(13.5), C-B(21), B-S(6.5), S-M(7) = 48

These are essentially the same cycle, just traversed in opposite directions.

Is there a way to get a shorter cycle? What if we don't use the expensive C-B edge (21 km)?

If we avoid C-B, we'd need another connection. But looking at the graph, to reach all 4 towns without using C-B, we'd have to... actually, we can't form a simple cycle without it because:
- M connects to S and C
- S connects to M, C, and B
- C connects to M, S, and B
- B connects to S and C

Without C-B, B only connects to S. So any path through B must go S-B-S, which means revisiting S. That's not efficient.

Wait, let me think again. If we allow revisiting nodes (which the problem doesn't explicitly forbid), could we do better?

M-S-B-S-C-M = 7 + 6.5 + 6.5 + 15 + 13.5 = 48.5 km (worse)

Or M-C-S-B-S-M = 13.5 + 15 + 6.5 + 6.5 + 7 = 48.5 km (worse)

So allowing revisits doesn't help.

What about: M-S-C-B-S-M? No, that revisits S.

I think 48 km is indeed the minimum. All valid circuits that visit each town exactly once and return to start give 48 km.

Final Answer:
1. 34.5 km
2. 35 km
3. 21.5 km
4. 48 km