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0580/43 May/Jun 2024, Question 7: Speed, Distance and Time

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 11 marks

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The question, in short

Work with three travel problems: find a journey time in minutes from distance and speed, bound a time from rounded values, and combine two speed stages into an overall average speed.

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Part (ai) · 2 marks

Given 50 km at 75 km/h, work out how long the trip takes and express it in minutes.

  1. 1Time = 50 ÷ 75 = 2/3 hour
  2. 22/3 × 60 = 40 minutes

Answer40

Part (aii) · 3 marks

With 47 km and 75 km/h both rounded, determine the smallest possible journey time in minutes.

  1. 1Lower bound distance = 46.5 km
  2. 2Upper bound speed = 77.5 km/h
  3. 3Lower bound time = 46.5 ÷ 77.5 = 0.6 h
  4. 40.6 × 60 = 36 minutes

Answer36

Part (b) · 6 marks

A 240 km trip has two stages: t minutes at 100 km/h then t + 60 minutes at 110 km/h; determine the overall average speed.

  1. 1t/60 × 100 + (t + 60)/60 × 110 = 240
  2. 2100t + 110t + 6600 = 14400
  3. 3210t = 7800, t = 37.14…
  4. 4Total time = 2t + 60 = 134.28… min = 2.238… h
  5. 5Average speed = 240 ÷ 2.238… = 107 km/h

Answer107 or 107.2…

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