Chapter 2.1, Problem 51E

The tortoise versus the hare: The speed of the hare is given by the sinusoidal function $H\left(t\right)=\text{1}-\text{cos}\left(\left(\pi \text{t}\right)/\text{2}\right)$ whereas the speed of the tortoise is $T\left(t\right)=\left(\text{l}/\text{2}\right){\text{tan}}^{-\text{1}}\left(\text{t}/\text{4}\right)$ ,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.