A bicyclist leaves from her home at 9am and rides to a beach 40 miles away. Because of a breeze off the ocean, the temperature at the beach remains 60 degrees F throughout the day. At the cyclist's home the temperature increases linearly with time, going from 60 degrees F at 9am to 80 degrees F by 1pm. 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 at town 10 mi from her home at 10am; 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 1pm, pedaling 20 mph.