Higher November 2022 Paper 1 Q13
13. Asha is taking part in a school cross-country race.
She:
- runs \(x\) km in 8 minutes, then
- walks 0·2 km in 2 minutes, then
- runs 1·8 km in 10 minutes.
Asha’s average speed for the whole race is \(\dfrac{5x + 2}{60}\) kilometres per minute.
Find the value of \(x\) and hence write the distance that she runs as a fraction of the total distance.
Give your answer in its simplest form. [6]
| Scheme | Marks | Comments |
|---|---|---|
| May be seen in parts | ||
| \(\dfrac{x+2}{20} = \dfrac{5x+2}{60}\) oe | B2 | B1 for \(\dfrac{x + 0.2 + 1.8}{8 + 2 + 10}\) oe |
| \(120 - 40 = 100x - 60x\) oe | M1 | FT ‘their derived equation’ provided of equivalent difficulty. |
| \((x =)\) 2 (km) oe | A1 | FT ‘their derived equation.’ |
| \(\dfrac{2 + 1.8}{2 + 0.2 + 1.8}\) oe or \(\left(1 - \dfrac{0.2}{2 + 0.2 + 1.8}\right)\) oe | M1 | FT ‘their derived 2’, if possible; do not ft negative values of \(x\) |
| \(\dfrac{19}{20}\) | A1 | FT provided simplification needed |
| (6) |