A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h, 45.0 min at 40 km/h and 12.0 min at 100 km/h, and spends 15.0 min eating lunch and buying gas. Determine the average sped for the trip. Determine the difference between the intial citties along the route.

Average speed of the trip = 52.9 km/h

Distance between initial pairs of cities (start to end) = 70.0 km

Explanation:

Since distance = speed * time

If she drives 30.0 min at 80.0 km/h

Distance covered = (30/60) * 80 = 40.0 km

Again she drives 45.0 min at 40 km/h

Distance covered = (45/60) * 40 = 30.0 km

Again she drives 12.0 min at 100 km/h

Distance covered = (12/60) * 100 = 20.0 km

Total distance covered = 40.0 + 30.0 + 20.0

= 90.0 km

Total time spent = 30.0 + 45.0 + 12.0 + 15.0

= 102 min

Average speed for the trip = Total distance covered/total time spent

= 90 / (102/60)

= 52.9 km/h

Distance between initial cities will be between the start of one city to the end of another

Between the first pairs = 40.0 + 30.0 = 70.0 km

Between the second pairs = 30.0 + 20.0 = 50.0 km