1. **State the problem:** Randy walks from Honiara (Point A) to Selwyn College (Point B), then to Lambi (Point C), stops for lunch and chatting, and returns to Honiara. We need to find: (a) The fastest part of Randy's journey. (b) Randy's speed on his return journey from Lambi to Honiara. 2. **Analyze the graph and given data:** - From A to B: Distance increases from 0 km to 20 km in 2 hours. - From B to C: Distance increases from 20 km to 30 km in 1 hour. - From C to A (return): Distance decreases from 30 km to 0 km in 4 hours. 3. **Calculate speeds for each part:** - Speed from A to B: $$\text{speed} = \frac{20 - 0}{2 - 0} = \frac{20}{2} = 10\text{ km/h}$$ - Speed from B to C: $$\text{speed} = \frac{30 - 20}{3 - 2} = \frac{10}{1} = 10\text{ km/h}$$ - Speed from C to A (return): $$\text{speed} = \frac{0 - 30}{7 - 3} = \frac{-30}{4} = -7.5\text{ km/h}$$ The negative sign indicates direction back to Honiara, so speed magnitude is 7.5 km/h. 4. **Answer (a):** The fastest part is the segment with the greatest speed. Both A to B and B to C have speed 10 km/h, which is faster than the return speed 7.5 km/h. 5. **Answer (b):** Randy's speed on the return journey from Lambi to Honiara is 7.5 km/h. **Final answers:** (a) The fastest part of Randy's journey was from Honiara to Selwyn College and from Selwyn College to Lambi, both at 10 km/h. (b) Randy's speed on his return journey was 7.5 km/h.