Chapter 6.1, Problem 51E

The tortoise versus the hare: The speed of the hare is given by the sinusoidal function $H\left(t\right)=1-\cos \left(\left(\pi t\right)/2\right)$ whereas the speed of the tortoise is $T\left(t\right)=\left(1/2\right){\tan }^{-1}\left(t/4\right)$, where t is time measured in hours and the speed is measured in miles per hour. Find the area between the curves from time t = 0 to the first time after one hour when the tortoise and hare are traveling at the same speed. What does it represent? Use a calculator to determine the intersection points, if necessary, accurate to three decimal places.