A bicyclist leaves from her home at 9 A.M. and rides to a beach 40mi away, Because of a breeze off the ocean, the temperature at the beach remains 58F throughout the day. At the cyclist's home the temperature increases linearly with time, going from 58F at 9 A.M. to 80F 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 10mi from her home at 10A.M :( (b) as she eatslunchat a rest stop 30 mi from her home at noon: (c) as she arrives enthusiastically at the beachat 1 P.M. pedaling 20mph (a) DT/Dt - (b) DT/Dt F/hr (c) DT/DT OF/hr