Question 6c (WASSCE 2008 May/June) A cyclist starts a journey at \( 10: 30 \mathrm{am} \) and lans to get home 45 km away by 3.00 pm . At irst, he traveled for 2 hours at \( 7 \frac{1}{2} \mathrm{kmh}^{-1} \) and hen \( x \mathrm{kmh}^{-1} \) for the rest the time in order to arrive promptly at home. Find the value of \( x \).

The cyclist travels for 2 hours at a speed of \( 7 \frac{1}{2} \, \text{km/h} \) (which is \( 7.5 \, \text{km/h} \)), covering a distance of \( 2 \times 7.5 = 15 \, \text{km} \). With a total journey distance of 45 km, he needs to cover \( 45 - 15 = 30 \, \text{km} \) in the remaining time. The entire journey from \( 10:30 \, \text{am} \) to \( 3:00 \, \text{pm} \) lasts for \( 4.5 \, \text{hours} \). After traveling for 2 hours, he has \( 4.5 - 2 = 2.5 \, \text{hours} \) left. Using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \), we find \( x \): \[ 30 = x \times 2.5 \] \[ x = \frac{30}{2.5} = 12 \, \text{km/h} \] So, the cyclist needs to travel at a speed of \( 12 \, \text{km/h} \) for the remainder of the journey. Not only is cycling a fun and environmentally friendly mode of transportation, but mastering different speeds can help a cyclist adjust to various terrains. For example, understanding when to pedal harder to tackle hills and when to ease off on flat roads can enhance stamina and overall performance. Every cyclist grapples with the challenge of pacing, especially during longer rides. A common mistake is starting too fast, leading to fatigue later on. To combat this, practice maintaining a steady speed during training rides, and consider using a cycling computer or app to track your pace. This way, you'll build endurance without burning out before the finish line!