1. **State the problem:** Tyler travels the first 10 miles in 20 minutes at a constant speed, and the rest of the journey in 50 minutes at another constant speed. We want to find which points A-I fit the distance-time graph for Tyler’s journey. 2. **Calculate speed for first part:** He travels 10 miles in 20 minutes. Convert 20 minutes to hours: $$20 \text{ min} = \frac{20}{60} = \frac{1}{3} \text{ hours}.$$ Speed for first part: $$v_1 = \frac{10 \text{ miles}}{\frac{1}{3} \text{ hours}} = 10 \times 3 = 30 \text{ miles per hour}.$$ 3. **Calculate distance at key times:** The journey starts at 10:30. 20 minutes later (at 10:50), Tyler has travelled 10 miles. So at 10:50, distance = 10 miles. 4. **Calculate speed for second part:** He travels the rest of the way (unknown distance) in 50 minutes. Let the total distance be $D$, so the remaining distance is $D - 10$ miles. 5. **Calculate speed for second part:** 50 minutes = $\frac{50}{60} = \frac{5}{6}$ hours. Speed for second part: $$v_2 = \frac{D - 10}{\frac{5}{6}} = (D - 10) \times \frac{6}{5}.$$ 6. **Distance-time graph segments:** - From 10:30 to 10:50 (20 mins): distance increases from 0 to 10 miles linearly. - From 10:50 to 11:40 (50 mins): distance increases from 10 miles to $D$ miles linearly. 7. **Check given points:** - Points must fall on either the first segment (0 to 10 miles, 10:30 to 10:50) or the second segment (10 to $D$ miles, 10:50 to 11:40). 8. **Check times and distances:** - Point G at (10:50, 10) lies exactly at the end of the first segment, so it lies on the graph. - Points A at (10:40, 20) and B at (10:50, 20) claim 20 miles where only a maximum of 10 miles is possible at those times, so they do not lie on the graph. - Points H at (11:00, 10) and I at (11:40, 10) show constant distance 10 after the first segment, but distance should be increasing, so these points are not on the graph. - Points C (11:20, 25), D (11:30, 25), E (11:40, 25), F (11:50, 25) all have distance 25 miles in the second segment or after it. We check if 25 miles is a reasonable total distance $D$. 9. **Determine total distance $D$:** The end of the journey is after 20 + 50 = 70 minutes, i.e. at 11:40. Since at 11:40, distance = $D$, and point E at (11:40, 25) lies on the graph, assume $D = 25$ miles. 10. **Conclusion:** Points on the graph are G (10:50, 10), C (11:20, 25), D (11:30, 25), E (11:40, 25). **Final answer:** Points G, C, D, E lie on the distance-time graph for Tyler's journey.