1. **Stating the problem:** Nanjala and Cherono start from Mwanzo towards Mwisho, which are 17 km apart. Nanjala walks at 9 km/h and starts 45 minutes before Cherono, who cycles at 30 km/h. We need to find the distance from Mwisho when Cherono catches Nanjala. 2. **Define variables and known values:** - Distance between Mwanzo and Mwisho: $17$ km - Nanjala's speed: $v_N = 9$ km/h - Cherono's speed: $v_C = 30$ km/h - Cherono starts $45$ minutes = $\frac{45}{60} = 0.75$ hours after Nanjala 3. **Calculate the head start distance of Nanjala:** $$\text{Distance}_{headstart} = v_N \times 0.75 = 9 \times 0.75 = 6.75 \text{ km}$$ 4. **Set up the equation for when Cherono catches Nanjala:** Let $t$ be the time in hours Cherono cycles before catching Nanjala. - Distance Nanjala covers after Cherono starts: $9t$ km - Distance Cherono covers after starting: $30t$ km Since Nanjala had a 6.75 km head start, Cherono catches Nanjala when: $$30t = 6.75 + 9t$$ 5. **Solve for $t$:** $$30t - 9t = 6.75$$ $$21t = 6.75$$ $$t = \frac{6.75}{21} = 0.3214 \text{ hours (approx)}$$ 6. **Calculate the distance Cherono travels before catching Nanjala:** $$d_C = 30 \times 0.3214 = 9.6429 \text{ km (approx)}$$ 7. **Calculate the distance from Mwisho when Cherono catches Nanjala:** Since they start at Mwanzo and the total distance is 17 km, $$\text{Distance from Mwisho} = 17 - d_C = 17 - 9.6429 = 7.3571 \text{ km (approx)}$$ **Final answer:** Cherono catches Nanjala approximately 7.36 km from Mwisho.