Water is entering at a rate of t cm3/s.
Suppose water is entering a series of vessels at the given rate. In each case, find the total amount of water entering during the first second, and the average rate during that time. Compare the average rate with rate at the "average time," at t = 0.5 halfway through the time period from 0 to 1. In which case is the average rate greater than the rate at the average time? Graph the flow rate function, and mark the flow rate at the average time. Can you guess what it is about the shape of the graph that determines how the average rate compares with the rate at the average time?