A bicyclist leaves from her home at 9 A.M. and rides to a beach \(40 \mathrm{mi}\) away. Because of a breeze off the ocean, the temperature at the beach remains \(60^{\circ} \mathrm{F}\) throughout the day. At the cyclist's home the temperature increases linearly with time, going from \(60^{\circ} \mathrm{F}\) at 9 A.M. to \(80^{\circ} \mathrm{F}\) 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 \(10 \mathrm{mph}\) through a town \(10 \mathrm{mi}\) from her home at 10 A.M.;

(b) as she eats lunch at a rest stop \(30 \mathrm{mi}\) from her home at noon;

(c) as she arrives enthusiastically at the beach at 1 P.M., pedaling \(20 \mathrm{mph}\).