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4MA1/1F Jun 2019, Question 15: Speed, Distance and Time

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 6 marks

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The question, in short

Use Jalina's distance-time graph for a cycle to a park to compare speeds, add her return journey, and find her average cycling speed excluding stops.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Decide whether she cycled faster before or after stopping at her friend's house, giving a reason from the graph.

  1. 1Before: 15 km in 1 hour = 15 km/h
  2. 2After: 9 km in 45 minutes = 9 ÷ 0.75 = 12 km/h
  3. 315 > 12 (the graph is steeper), so before

Answerbefore

Part (b) · 2 marks

Add to the graph her 45-minute stay at the park and a constant 16 km/h return ride home.

  1. 1Jalina stayed at the park until 12:45, so horizontal line from (12:00, 24) to (12:45, 24)
  2. 2She cycled back at 16 km/h over 24 km
  3. 3Time = 24 ÷ 16 = 1.5 hours = 1 hour 30 minutes
  4. 412:45 + 1 hour 30 minutes = 14:15
  5. 5So draw line from (12:45, 24) to (14:15, 0)

Answerline from (12:00, 24) to (12:45, 24) to (14:15, 0)

Part (c) · 3 marks

Calculate her average cycling speed in km/h for the whole trip, excluding non-cycling time, to 1 decimal place.

  1. 1To the park: 24 km in 2 hours minus the 15-minute stop = 1.75 hours
  2. 2Back home: 24 ÷ 16 = 1.5 hours
  3. 3Total: 48 km in 1.75 + 1.5 = 3.25 hours
  4. 4Average speed = 48 ÷ 3.25 = 14.769… = 14.8

Answer14.8

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