$2-5$ A person travels by car from one city to another with different constant speeds between pairs of cities. She drives $37\mathrm{.}3$min at $83\mathrm{.}7k\frac{m}{h},11\mathrm{.}8$min at $126k\frac{m}{h},$ and $45\mathrm{.}5$min at $37\mathrm{.}7k\frac{m}{h},$ and spends $15\mathrm{.}1$min eating lunch and buying gas.

$($a$)$ Determine the distance between the initial and final cities along this route.

$km(+-0\mathrm{.}2km)$

$($b$)$ Determine the average speed for the trip.

$k\frac{m}{h}(+-0\mathrm{.}2k\frac{m}{h})$

Source: Serway and Faughn, College Physics, $5$th edition, Problem $2\mathrm{.}1$

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