A person travels by car from one city to another with different constant speeds between

pair of cities. She drives for 31.5 min at
89.6 km/h, 11.8 min at 101.8 km/h, and
58.5 min at 36.4 km/h, and spends 24.8 min
eating lunch and buying gas.
Find the distance between the initial and
final cities along this route.
Answer in units of km

Dt=89.6km/60min*31.5min+

101.8km/60min*11.8min+36.4km/60min*58.5=
Tot. Dist.

T = t1 + t2 + t3 + t4. = Tot. min.
T/60min/h = T in hours.
r(avg) = Dt/T

To find the distance between the initial and final cities along this route, we need to calculate the total distance traveled during each segment of the journey.

First, let's calculate the distance traveled during each segment.

In the first segment, the person travels for 31.5 minutes at a speed of 89.6 km/h. To find the distance traveled, we use the formula: distance = speed × time.

distance1 = 89.6 km/h × (31.5 min / 60 min/h) = 46.92 km

In the second segment, the person travels for 11.8 minutes at a speed of 101.8 km/h. Calculating the distance:

distance2 = 101.8 km/h × (11.8 min / 60 min/h) = 20.06 km

For the third segment, the person travels for 58.5 minutes at a speed of 36.4 km/h. Calculating the distance:

distance3 = 36.4 km/h × (58.5 min / 60 min/h) = 35.81 km

Now, let's calculate the total distance traveled:

total distance = distance1 + distance2 + distance3
= 46.92 km + 20.06 km + 35.81 km
= 102.79 km

Therefore, the distance between the initial and final cities along this route is approximately 102.79 km.