NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Relationships between variables

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Two students, Alex and Jordan, walk different routes from their homes to the same school in Melbourne. Alex walks at a constant speed and covers 3900 metres in 30 minutes.

Jordan walks at a constant speed and covers 7400 metres in 50 minutes. What is the difference in their walking speeds in metres per minute?

Express your answer as an exact fraction.

Concept illustrations

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Association between paired values. Authored example pairs show a positive association: larger x tends to accompany larger y. A scatterplot alone cannot establish causation. Axes show arbitrary numerical units.xyPaired observations
Authored example pairs show a positive association: larger x tends to accompany larger y. A scatterplot alone cannot establish causation. Axes show arbitrary numerical units.
A straight-line relationship. Illustration: y = x + 1. Each unit right adds one unit up; the y-intercept is 1.-2-2-1-111223344xy
Illustration: y = x + 1. Each unit right adds one unit up; the y-intercept is 1.

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Worked solution and answer (click to reveal)

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Worked solution

  1. Alex walks 3900 metres in 30 minutes. To find Alex's speed, divide distance by time: 3900 ÷ 30.
  2. 3900 ÷ 30 = 130. So Alex's speed is 130 metres per minute.
  3. Jordan walks 7400 metres in 50 minutes. To find Jordan's speed, divide distance by time: 7400 ÷ 50.
  4. 7400 ÷ 50 = 148. So Jordan's speed is 148 metres per minute.
  5. The difference in their speeds is 148 - 130 = 18 metres per minute.
  6. Express 18 as a fraction: 18/1. This is already in simplest form.
  7. Check that both speeds were calculated correctly using division: 30 × 130 = 3900 and 50 × 148 = 7400.
  8. The question asks for the difference in speeds as an exact fraction. 18/1 is exact.
  9. No further simplification is needed since 18 and 1 have no common factors other than 1.
  10. The difference in walking speeds is 18 metres per minute, expressed as 18/1.
  11. Final answer: 18/1 metres per minute.
  12. The result is exact and matches the required format: an exact fraction in metres per minute.

Reference answer: 18/1

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