Final answer:
Enrique is correct because the average rate of change for any part of a trip cannot be greater than the entire trip's average rate of change, unless it's offset by a lower rate in another part, while still taking into account the whole trip's average.
Step-by-step explanation:
Enrique's statement about the average rate of change for any part of his trip not being greater than the average rate of change for the whole trip can be explained with mathematics. The average rate of change over an interval is calculated by taking the difference in the value of the function at the end and start of the interval and dividing by the length of the interval. When we consider the entire trip as one interval, any part of the trip will have its own rate of change. If the rate of change for the whole trip is the highest possible, then any specific part cannot have a higher rate without affecting the overall average, unless it's balanced by a lower rate in another part.
Consider an analogy: If you drive for two hours, the first hour at 50 km/h and the second at 70 km/h, your average speed for the whole trip would be (50+70)/2 = 60 km/h. The average rate for any one hour is less than or equal to 70 km/h. A higher average would mean you'd have to have driven at more than 70 km/h for one of the hours, which is not possible in this instance since 70 km/h is the maximum.