Solving Rectilinear Problems - Example Problem 2.3-4

A bicyclist pedals his bike to produce a constant speed of 20 mph on level ground for 0.5 miles. At this point, he encounters a 0.5 mile hill and his speed decreases as v = (1/s⁴) + 4 mph. After cresting the hill, he accelerates downhill for 1 mile. His speed over the 2 miles is shown in the graph. Determine the total time it takes the cyclist to traverse the 2 miles.

Given: