4MA1/2HR Jun 2022, Question 18: Upper and Lower Bounds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Using rounded distance and time values for two car journeys, work out bounds on each average speed and show that Kaidan's speed could exceed Sonja's.
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Solution · 4 marks
- 1Upper bound for Kaidan's distance = 82.5 km
- 2Lower bound for Kaidan's time = 2.65 hours
- 3Upper bound for Kaidan's average speed = 82.5 ÷ 2.65 = 31.13 km/h
- 4Lower bound for Sonja's distance = 32.5 km
- 5Upper bound for Sonja's time = 1.05 hours
- 6Lower bound for Sonja's average speed = 32.5 ÷ 1.05 = 30.95 km/h
- 731.13 > 30.95
- 8Kaidan's average speed could have been greater than Sonja's
AnswerKaidan's greatest speed is 82.5 ÷ 2.65 = 31.13 km/h and Sonja's least speed is 32.5 ÷ 1.05 = 30.95 km/h, so Kaidan's could be greater
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