A bicyclist leaves from her home at 9 A.M. and rides to a beach 40 mi away. Because of a breeze off the ocean, the temperature at the beach remains 64 oF throughout the day. At the cyclist's home the temperature increases linearly with time, going from 64 oF at 9 A.M. to by 80 oF 1 P.M. The temperature is assumed to vary linearly as a function of position between the cyclist's home and the beach. Determine the rate of change of temperature observed by the cyclist for the following conditions: (a) as she pedals 10 mph through a town 10 mi from her home at 10 A.M.; (b) as she eats lunch at a rest stop 30 mi from her home at noon; (c) as she arrives enthusiastically at the beach at 1 P.M., pedaling 20 mph.