The distance-time graph shows a hiker's walk from a car park to a summit, a rest, and the walk back down. 40 55 85 6 Time (minutes) Distance (km) © EAGLE BE...

Distance-time graphs made of several straight sections can be read section by section: speed on each moving section is distance divided by time (converted to hours), and a flat section means resting.

1. Reading directly from the graph, after \(40\) minutes the hiker has covered \(6\) km, so they are \(6\) km from the car park. [1]
2. The \(6\) km climb takes \(40\) minutes \(= \dfrac{2}{3}\) hour: \[6 \div \dfrac{2}{3} = 9 \text{ km/h}\] [2]
3. The graph is flat from \(40\) to \(55\) minutes: the hiker is resting at the summit, for \(55 - 40 = 15\) minutes. [2] (correct activity identified, correct duration)
4. The walk back down covers the same \(6\) km between \(55\) and \(85\) minutes, a duration of \(30\) minutes \(= 0.5\) hour: \[6 \div 0.5 = 12 \text{ km/h}\] [3]
5. Comparing the two speeds: \[12 \div 9 = 1.33 \text{ (2 d.p.)}\] The walk down was about \(1.33\) times as fast as the walk up, not twice as fast, so the hiker's claim of feeling "about twice as fast" is not numerically justified. [4] (correct ratio calculated, correct comparison to double, correct conclusion)

"Twice as fast" is a precise numerical claim; check it by dividing the two speeds rather than relying on how different they feel, since a genuinely faster walk, here by about a third, can still fall well short of being double.