Chapter 6.1, Problem 52E

The tortoise versus the hare: The speed of the hare is given by the sinusoidal function $H\left(t\right)=\left(1/2\right)-\left(1/2\right)\cos \left(2\pi t\right)$ whereas the speed of the tortoise is $T\left(t\right)=\sqrt{t}$, where t is time measured in hours and speed is measured in kilometers per hour. If the race is over in 1 hour, who won the race and by how much? Use a calculator to determine the intersection points, if necessary, accurate to three decimal places.