A person travels by car from one city to another with different constant speeds between pair of cities. She drives for 38.6 min at 87.2 km/h, 10.3 min at 107.9 km/h, and 45.6 min at 45.7 km/h, and spends 17.9 min eating lunch and buying gas.

Find the distance between the initial and final cities along this route. Answer in units of km.

Find the average speed for the trip. Answer in units of km/h.

do distance=rate*time for each leg, then add the distances. Change min to hour by dividing by 60.

To find the distance between the initial and final cities along this route, we need to find the sum of the distances traveled at each speed.

First, we need to convert the times from minutes to hours so that they have the same unit as the speeds.

38.6 minutes = 38.6 / 60 = 0.6433 hours
10.3 minutes = 10.3 / 60 = 0.1717 hours
45.6 minutes = 45.6 / 60 = 0.76 hours
17.9 minutes = 17.9 / 60 = 0.2983 hours

Next, we calculate the distances traveled at each speed using the formula: distance = speed * time.

Distance at 87.2 km/h = 87.2 km/h * 0.6433 hours = 56.1376 km
Distance at 107.9 km/h = 107.9 km/h * 0.1717 hours = 18.52843 km
Distance at 45.7 km/h = 45.7 km/h * 0.76 hours = 34.732 km

Since the person traveled from one city to another, the distance between the initial and final cities is the sum of the distances traveled at each speed.

Total distance = 56.1376 km + 18.52843 km + 34.732 km = 109.39703 km

Therefore, the distance between the initial and final cities along this route is 109.39703 km.

To find the average speed for the trip, divide the total distance by the total time taken, including the time spent eating lunch and buying gas.

Total time = 0.6433 hours + 0.1717 hours + 0.76 hours + 0.2983 hours = 1.8733 hours

Average speed = Total distance / Total time = 109.39703 km / 1.8733 hours ≈ 58.36 km/h

Therefore, the average speed for the trip is approximately 58.36 km/h.