Question

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 55.0 min at 80.0 km/h, 10.0 min at 70 km/h, and 55.0 min at 55.0 km/h, and spends 55.0 min eating lunch and buying gas.
(a) Determine the average speed for the trip.

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

Answer 1

Part a

The average speed = total distance traveled upon total time taken.

we know, distance =speed × time

Average speed = $\frac{S_1t_1+S_2t_2+S_3t_3}{t_1+t_2+t_3+t_4}$

insert the values:

$S_1=80 km/hr\\ S_2=70 km/hr\\ S_3=55km/hr\\ t_1=55 min\\ t_2=10min\\ t_3=55min\\ t_4=55min$

$\frac{80\times 55+70\times10+55\times 55}{55+10+55+55} km/hr$

= $\frac{8125}{175}$ km/hr

= 46.43 km/hr

Hence, the average speed for the trip is 46.43 km/hr.

Part b

the total distance between two cities via this route would be the average speed times the total time taken = 46.43 km/hr × 2.9 hr = 134.65 km

(because 175 minutes = 2.9 hours)

Hence, the total distance between two cities via this route is 134.65 km.