The research and development department of an automobile manufacturer determines that when a driver is required to stop quickly to avoid an accident, the distance (in feet) the car travels during the driver's reaction time is given by R(x) = 3/4x, where x is the speed of the car in miles per hour. The distance (in feet) the car travels while the driver is braking is given by B(x) = 1/15 x2.
(a) Find the function that represents the total stopping distance T.
(b) Graph the functions R, B, and T on the same set of coordinate axes for 0 ≤ x ≤ 60.
(c) Which function contributes most to the magnitude of the sum at higher speeds? Explain.