NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Ratio modelling

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A walking route in Sydney is designed to include three segments: a flat path, a gentle incline, and a steep climb. The ratio of the flat path length to the incline length to the steep climb length is 13 : 20 : 7.

If the total length of the route is 1440 metres, what is the exact length, in metres, of the steep climb segment? Express your answer as an exact fraction or whole number.

Concept illustrations

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Two red counters for every three blue counters. Red:blue = 2:3. There are 5 counters in all, so the red fraction of the whole is 2/5.RedRedBlueBlueBlue2 red : 3 blue · 5 counters in all
Red:blue = 2:3. There are 5 counters in all, so the red fraction of the whole is 2/5.
Translate a situation into a model. With a fixed charge of $4 and $2 per kilometre, cost C = 4 + 2d. At d = 3 km the cost is $10. Assume this tariff applies for the trip.$4 + $2/kmDefine tariff→C = 4 + 2dBuild rule→d=3 → C=$10Interpret
With a fixed charge of $4 and $2 per kilometre, cost C = 4 + 2d. At d = 3 km the cost is $10. Assume this tariff applies for the trip.

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Worked solution

  1. The ratio of flat path : incline : steep climb is given as 13 : 20 : 7.
  2. The total parts in the ratio are 13 + 20 + 7 = 40 parts.
  3. The total length of the route is 1440 metres, which corresponds to 40 parts.
  4. To find the length of one part, divide the total length by the total number of parts: 1440 ÷ 40 = 36 metres per part.
  5. The steep climb segment corresponds to 7 parts.
  6. Multiply the length per part by the number of parts for the steep climb: 7 × 36 = 252 metres.
  7. Check: 13 parts (flat) = 13 × 36 = 468 m, 20 parts (incline) = 20 × 36 = 720 m, 7 parts (steep) = 252 m.
  8. Add the segments: 468 + 720 + 252 = 1440 m, which matches the total route length.
  9. The calculation is consistent and the total length is correct.
  10. Therefore, the steep climb segment is exactly 252 metres.

Reference answer: 252 m

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