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 60 ° f throughout the day. at the cyclist's home the temperature increases linearly with time, going from 60 ° f at 9 a. m. to 80 ° f 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.