1. The problem asks to find how long Lottie stays at Fatoumata's house based on the distance-time graph. 2. From the graph, Lottie starts at home (0 km) at 12:00 and travels to Fatoumata's house, reaching 40 km at 13:00. 3. She stays at Fatoumata's house while the distance remains constant at 40 km from 13:00 to 13:30. 4. Then, she travels back home, with the distance decreasing from 40 km at 13:30 to 0 km at 14:00. 5. The time Lottie stays at Fatoumata's house is the duration when the distance does not change, which is from 13:00 to 13:30. 6. Calculate the time difference: $$13:30 - 13:00 = 0.5\text{ hours} = 30\text{ minutes}.$$ Final answer: Lottie stays at Fatoumata's house for 30 minutes.