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

Explanation:

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

`V=(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=(v_1t_1+v_2t_2+v_3t_3+v_4t_4)/(t_1+t_2+t_3+t_4)\\\\V=(95* (60)/(60)+55* (10)/(60)+45* (35)/(60)+0* 50)/((60)/(60)+(10)/(60)+(35)/(60)+(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* (60)/(60)+55* (10)/(60)+45* (35)/(60)+0* 50\\\\D=130.41\ \text{km}`

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