1. **State the problem:** Beth drives a total of 200 miles in 4 hours. She drives the first 18 miles at 36 mph. We need to find her average speed for the remaining part of the journey. 2. **Calculate time taken for the first 18 miles:** Speed = 36 mph Distance = 18 miles Time = Distance / Speed = $\frac{18}{36} = 0.5$ hours 3. **Calculate distance and time remaining:** Total distance = 200 miles Distance remaining = $200 - 18 = 182$ miles Total time = 4 hours Time remaining = $4 - 0.5 = 3.5$ hours 4. **Calculate average speed for the remaining journey:** Average speed = Distance remaining / Time remaining = $\frac{182}{3.5} = 52$ mph **Final answer:** Beth's average speed for the rest of the journey is $52$ mph.