3. (10 points) A bicyclist leaves her home at 9 A.M. and rides 40 mi to a beach. Because of an ocean breeze, 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, in /hr, observed by the cyclist for the following conditions: (a) as she pedals 10 mph through a town (on the way to the beach) 10 mi from her home at 10 A.M. (b) as she eats lunch at a rest stop 30 mi from he home at noon (c) as she arrives enthusiastically at the beach at 1 P.M., pedaling 20 mph.

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