NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Exploring linear functions

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Two friends, Sam and Tanya, start walking from the same point in Melbourne along a straight path. Sam walks at a constant speed of 63 metres per minute, and Tanya walks at 41 metres per minute, both in the same direction.

After how many minutes will the distance between them be exactly 1260 metres? Give your answer as an exact fraction.

Concept illustrations

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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.
Keep both sides balanced. The level beam represents equality, not measured weights. Subtract 6 from both sides of x + 6 = 14 to leave x = 8.x + 614−6−6x = 8
The level beam represents equality, not measured weights. Subtract 6 from both sides of x + 6 = 14 to leave x = 8.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. Sam walks at 63 metres per minute, Tanya at 41 metres per minute, both in the same direction from the same starting point in Melbourne.
  2. The relative speed between Sam and Tanya is the difference in their speeds: 63 m/min - 41 m/min = 22 m/min.
  3. The distance between them increases at a rate of 22 metres per minute.
  4. We need to find the time when this distance reaches exactly 1260 metres.
  5. Use the formula: time = distance / relative speed.
  6. Substitute values: time = 1260 m / 22 m/min.
  7. Simplify the fraction: 1260 / 22.
  8. Divide numerator and denominator by 2: 630 / 11.
  9. 630 ÷ 11 = 57.2727..., but we keep the exact fraction: 630/11 minutes.
  10. Check: 630/11 × 22 = (630 × 22) / 11 = 630 × 2 = 1260 metres. Correct.
  11. The time when the distance between them is exactly 1260 metres is 630/11 minutes.
  12. Final answer: 630/11 minutes.

Reference answer: 630/11

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