NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Spatial problem-solving algorithms

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A city planner in Perth is designing a pedestrian route network using digital mapping software. The network is modelled as a weighted graph with five key nodes: the Perth Cultural Centre (PCC), the Art Gallery (AG), the State Library (SL), the Barrack Street Jetty (BJ), and the Elizabeth Quay (EQ).

The planner uses a shortest-path algorithm to compare two distinct walking routes from PCC to EQ, both of which pass through AG and SL in sequence. Route 1: PCC → AG → SL → BJ → EQ.

Route 2: PCC → AG → SL → EQ (direct). The walking distances (in metres) are as follows: PCC to AG = 490 m, AG to SL = 900 m, SL to BJ = 490 m, BJ to EQ = 900 m, and SL to EQ = 1300 m.

The planner uses a digital algorithm to compute the exact total length of Route 1.

What is the exact total length of Route 1 in metres?

Concept illustrations

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The problem requires calculating the total walking distance for Route 1: PCC → AG → SL → BJ → EQ.
  2. The distances between nodes are given in metres: PCC to AG = 490 m, AG to SL = 900 m, SL to BJ = 490 m, BJ to EQ = 900 m.
  3. The total length of Route 1 is the sum of the individual segment distances.
  4. Substitute the given values into the sum: 490 + 900 + 490 + 900.
  5. Perform the addition step by step: 490 + 900 = 1390.
  6. 1390 + 490 = 1880.
  7. 1880 + 900 = 2780.
  8. The total length of Route 1 is 2780 metres.
  9. Verify the addition: 490 + 490 = 980, 900 + 900 = 1800, 980 + 1800 = 2780.
  10. The result is consistent and matches the sum of all segments.
  11. The exact total length of Route 1 is 2780 metres.
  12. The answer is confirmed and matches the required unit (metres).

Reference answer: 2780 m

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