1. **State the problem:** Cheryl travels a total distance of 6 km. She travels the first 3 km at 40 km/hr. We need to find the speed for the remaining 3 km so that her average speed for the entire 6 km is 60 km/hr. 2. **Recall the formula for average speed:** $$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$$ 3. **Calculate total time needed to average 60 km/hr over 6 km:** $$\text{Total time} = \frac{\text{Total distance}}{\text{Average speed}} = \frac{6}{60} = 0.1 \text{ hours}$$ 4. **Calculate time taken for the first 3 km at 40 km/hr:** $$t_1 = \frac{3}{40} = 0.075 \text{ hours}$$ 5. **Calculate time left for the remaining 3 km:** $$t_2 = \text{Total time} - t_1 = 0.1 - 0.075 = 0.025 \text{ hours}$$ 6. **Calculate required speed for the remaining 3 km:** $$v_2 = \frac{\text{Distance}}{\text{Time}} = \frac{3}{0.025} = 120 \text{ km/hr}$$ **Final answer:** Cheryl must travel the remaining 3 km at **120 km/hr** to average 60 km/hr for the entire trip.