Foundation June 2022 Paper 3 Q28
28 Tom and Adil are the two runners in a 200-metre race.
Tom completes the race in 24 seconds.
Adil completes the race at an average speed of 28.8 kilometres per hour.
Who wins the race?
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – compares speeds in m/s | ||
| \(200 \div 24\) or 8.3(3…) | M1 | oe eg \(\dfrac{200}{24}\) or \(8\dfrac{1}{3}\) |
| \(28.8 \times 1000 \div 60 \div 60\) or 8 | M1 | oe eg \(28\,800 \div 3600\) or \(28.8 \div 3.6\) |
| 8 and 8.3(3…) and Tom | A1 | oe eg 8 and \(8\dfrac{1}{3}\) and Tom |
| Alternative method 2 – compares speeds in km/h | ||
| \(200 \div 24\) or 8.3(3…) | M1 | oe eg \(\dfrac{200}{24}\) or \(8\dfrac{1}{3}\) |
| their \(8.3(3\ldots) \div 1000 \times 60 \times 60\) or 30 | M1dep | oe eg \(0.008\,3(3\ldots) \times 3600\) |
| 30 and Tom | A1 | |
| Alternative method 3 – time for Adil starting with m/s | ||
| \(28.8 \times 1000 \div 60 \div 60\) or 8 | M1 | oe eg \(28\,800 \div 3600\) |
| \(200 \div\) their 8 or 25 | M1dep | oe eg \(\dfrac{200}{8}\) |
| 25 and Tom | A1 | oe eg Tom by 1s |
| Alternative method 4 – time for Adil starting with km/h | ||
| \(\dfrac{200 \div 1000}{28.8}\) or [0.0069, 0.007] or \(\dfrac{200}{28.8}\) or [6.9, 7] | M1 | oe eg \(\dfrac{0.2}{28.8}\) eg \(\dfrac{125}{18}\) |
| their [0.0069, 0.007] \(\times 60 \times 60\) or their [6.9, 7] \(\div 1000 \times 60 \times 60\) or 25 | M1dep | oe eg \(\dfrac{0.2}{28.8} \times 3600\) |
| 25 and Tom | A1 | oe eg Tom by 1s |
| Alternative method 5 – distance for Adil in 24s | ||
| \(28\,800 \times 24\) or 691 200 or \(28.8 \div 60 \div 60\) or 0.008 or \(28.8 \times 24\) or 691.2 | M1 | oe eg \(\dfrac{3456}{5}\) |
| their \(691\,200 \div 60 \div 60\) or their \(0.008 \times 1000 \times 24\) or their \(691.2 \times 1000 \div 60 \div 60\) or 192 | M1dep | oe eg \(28\,800 \times 24 \div 3600\) |
| 192 and Tom | A1 | |
Additional guidance
| Up to M2 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts | |
| Ignore all units | |
| Allow other correct comparisons | |
| eg 500 and 480 (this is metres per minute) | M1M1 |
| eg 500 and 480 and Tom | M1M1A1 |
| 200 m = 0.2 km, 24 s = \(24 \div 60 \div 60 = \dfrac{1}{150}\) hour, \(0.2 \div \dfrac{1}{150} = 30\) and Tom | M1M1A1 |
| \(\dfrac{200 \div 1000}{24} = \dfrac{1}{120}\) (or 0.0083…) | M1 |