1. The problem states a cyclist travels 20 km at an average speed of $x$ km/h. 2. (a) The time taken for this journey is distance divided by speed, which is $$\frac{20}{x}$$ hours. 3. (b) If the speed increases by 5 km/h, the new speed is $x + 5$ km/h, so the time taken would be $$\frac{20}{x+5}$$ hours. 4. (c) The problem states that the time difference between the two journeys is 40 minutes, or $\frac{40}{60} = \frac{2}{3}$ hours. 5. Therefore, the equation representing this is: $$\frac{20}{x} - \frac{20}{x + 5} = \frac{2}{3}$$ This shows the time saved by increasing the speed by 5 km/h is exactly 2/3 hours (40 minutes).