Question

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 60.0 min at 95.0 km/h, 10.0 min at 55.0 km/h, and 35.0 min at 45.0 km/h and spends 50.0 min eating lunch and buying gas.
(a) Determine the average speed for the trip. km/h
(b) Determine the distance between the initial and final cities along the route. km

Answer 1

Step-by-step explanation:

(a) The average speed of a person for the trip is given by total distance traveled divided by total time taken.

$V=\dfrac{d_1+d_2+d_3+d_4}{t_1+t_2+t_3+t_4}$

Since, distance = velocity × time

Also, 1 hour = 60 min

$V=\dfrac{v_1t_1+v_2t_2+v_3t_3+v_4t_4}{t_1+t_2+t_3+t_4}\\\\V=\dfrac{95\times \dfrac{60}{60}+55\times \dfrac{10}{60}+45\times \dfrac{35}{60}+0\times 50}{\dfrac{60}{60}+\dfrac{10}{60}+\dfrac{35}{60}+\dfrac{50}{60}}\\\\V=50.48\ \text{km/h}$

The average speed for the trip is 50.48 km/h

(b) Total distance,

$D=v_1t_1+v_2t_2+v_3t_3+v_4t_4\\\\D=95\times \dfrac{60}{60}+55\times \dfrac{10}{60}+45\times \dfrac{35}{60}+0\times 50\\\\D=130.41\ \text{km}$

The distance between the initial and final cities along the route is 130.41 km.