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 100.0 km/h, 14.0 min at 65.0 km/h, and 45.0 min at 60.0 km/h and spends 20.0 min eating lunch and buying gas. (a) Determine the average speed for the trip.

To find the average speed for the trip, we need to divide the total distance traveled by the total time taken.

First, we need to calculate the distance traveled during each leg of the trip.

For the first leg, the person drives for 55.0 minutes at 100.0 km/h. We can calculate the distance as follows:

Distance = Speed * Time
Distance = 100.0 km/h * (55.0 min / 60 min) [converting minutes to hours]
Distance = 91.7 km

For the second leg, the person drives for 14.0 minutes at 65.0 km/h. Again, we can calculate the distance:

Distance = Speed * Time
Distance = 65.0 km/h * (14.0 min / 60 min) [converting minutes to hours]
Distance = 15.8 km

For the third leg, the person drives for 45.0 minutes at 60.0 km/h. Calculating the distance:

Distance = Speed * Time
Distance = 60.0 km/h * (45.0 min / 60 min) [converting minutes to hours]
Distance = 45.0 km

Now, let's calculate the total distance:

Total Distance = Distance of first leg + Distance of second leg + Distance of third leg
Total Distance = 91.7 km + 15.8 km + 45.0 km
Total Distance = 152.5 km

Next, we need to calculate the total time taken:

Total Time = Time for first leg + Time for second leg + Time for third leg + Time for lunch and gas
Total Time = 55.0 min + 14.0 min + 45.0 min + 20.0 min
Total Time = 134.0 min

Finally, we can find the average speed by dividing the total distance by the total time:

Average Speed = Total Distance / Total Time
Average Speed = 152.5 km / (134.0 min / 60 min) [converting minutes to hours]
Average Speed = 68.21 km/h

Therefore, the average speed for the trip is 68.21 km/h.

\boxed{68.21 \, \text{km/h}}