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 66 oF throughout the day. At the cyclist's home the temperature increases linearly with time, going from 66 oF at 9 A.M. to 80 oF by 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.