Question

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 35.0 min at 100.0 km/h, 10.0 min at 55.0 km/h, and 45.0 min at 35.0 km/h and spends 35.0 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:

Solution:

Let the time be

t1=35min = 0.58min

t2=10min=0.166min

t3=45min= 0.75min

t4=35min= 0.58min

let the velocities be

v1=100km/h

v2=55km/h

v3=35km/h

a. Determine the average speed for the trip. km/h

first we have to solve for the distance

S=s1+s2+s3

S= v1t1+v2t2+v3t3

S= 100*0.58+55*0.166+35*0.75

S=58+9.13+26.25

S=93.38km

V=S/t1+t2+t3+t4

V=93.38/0.58+0.166+0.75+0.58

V=93.38/2.076

V=44.98km/h

b. the distance is 93.38km