Higher June 2022 Paper 2 Q9
9. Bronny takes part in a triathlon.
In this race she:
- swims 1·5 km in \(\frac{3}{4}\) hour,
- cycles at an average speed of 27 km/h for 1 hour and 30 minutes,
- runs 9 km in 1 hour.
The average speed of the winner of the triathlon is 16·1 km/h.
Show that Bronny does not win the race. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \(27 \times 1.5\) oe | M1 | Allow \(27 \times 1.3\) |
| 40.5 | A1 | CAO May be implied in total distance (51) later. |
| \(\dfrac{1.5 + 40.5 + 9}{0.75 + 1.5 + 1}\ \left(= \dfrac{51}{3.25}\right)\) | m1 | Must be using km and hours FT ‘their 40.5’ Allow m1 but A0 for \(\dfrac{1.5 + \text{their } 40.5 + 9}{3.15}\) |
| 15.6(9..) or 15.7 km/h (< 16.1 km/h) | A1 | FT provided the answer is less than 16.1 |
Alternative method 1 for final 2 marks
| Scheme | Marks | Comments |
|---|---|---|
| (winning time =) \(\dfrac{1.5 + 40.5 + 9}{16.1}\) oe | m1 | FT ‘their 40.5’ including the correct use of 1.3 hours |
| 3.1(6...) (hours) < 3.25 (hours) | A1 | A0 unless the 3.25 hours seen |
Alternative method 2 for final 2 marks
| Scheme | Marks | Comments |
|---|---|---|
| (Possible distance travelled by winner =) \(16.1 \times 3.25\) AND (Length of race = ) \(1.5 + 40.5 + 9\) | m1 | FT ‘their 40.5’ |
| 52(.325 (km) > 51 (km) | A1 |
| (4) |