The Big Five Marathon is an annual event in South Africa - NSC Mathematical Literacy - Question 3 - 2018 - Paper 2

The general direction a marathon runner is heading when passing the 20 km mark is South East. This direction indicates a typical course layout for marathons in similar regions.

The runner is correct if he is at a point on the marathon route that reaches the highest elevation, specifically at a mark of 1,708 meters, which is the highest point above sea level in the race course. This ensures that he is indeed at the highest elevation point, as indicated by the race map.

Cut-off times are implemented to ensure the safety and well-being of runners, manage logistical aspects of the race, and to allow sufficient time for the event to be completed. They help organizers prepare for future events while ensuring that all participants are equipped to finish the race within a reasonable time.

To verify the runner's claim, first, we need to calculate the speed required for the full marathon to meet the cut-off time:

1. Distance covered for full marathon: 42 km
2. Total time before cut-off: 7 hours (or 7 hours = 420 minutes)
3. Required speed: $\text{Required Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{42 \text{ km}}{7 \text{ hours}} = 6 \text{ km/h}$

Now, consider the half-marathon speed:

1. Distance for half-marathon: 21 km
2. Cut-off time: 5 hours (or 5 hours = 300 minutes)
3. Speed for half-marathon: $\text{Speed} = \frac{21 \text{ km}}{5 \text{ hours}} = 4.2 \text{ km/h}$

Finally, check if the marathon runner's assertion is correct with the comparison of speeds:

• He states he must run 2.7 km/h faster than the speed of the half-marathon runner: $\text{Marathon Speed} = 4.2 \text{ km/h} + 2.7 \text{ km/h} = 6.9 \text{ km/h}$

Since 6.9 km/h is greater than the required 6 km/h, he can indeed run 2.7 km/h faster to meet the cut-off time. Therefore, the runner is incorrect in his assertion.