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 50.0 km/h, 13.0 min at 75.0 km/h, and 30.0 min at 55.0 km/h and spends 15.0 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)

(a) Total distance = (50*0.917) + (75*0.217) + (55*0.5) + (0*0.25) = 89.6 km
total time taken = 55+13+30+15 = 113 minutes = 1.88 hours
average speed = 89.6/1.88 = 47.6 km/h

(b) 89.6 km

As for average, remember that there are three types of average used: mean, median, and mode. Mode is whichever occurs the most. In this case 50 km/h would be the mode per minute. The median is whichever has the same amount both greater and smaller (like the middle). In this case the median would be 50 km/h since it has just as much time on the trip going slower per minute as it does faster. Now we look at the mean, which is the traditional add all the numbers and then divide by the amount of numbers added. (55x50+13x75+30x55+15x0)/113=47.57km/h
(note: if you ate just looking for the mean of the speeds themselves and not of the whole trip, speed multiplied by time at that speed divided by total time, then the answer would be 45, which is the five speeds added and divided by 5.
The distance is 113.

Average speed = Total Distance/ Total Time

First convert the speeds into km/min. Because the time unit is in minutes.

50 km/h = 0.83 km/min
75 km/h = 1.25 km/min
55 km/h = 0.92 km/min

then calculate the total distance which is = (0.83 * 55) + (1.25 * 13) + (0.92 * 30) km = 89.5 km

total time = 113 mins
convert the time into hours which is 1.88 hr

therefore, the average speed = 89.5 km/1.88 hr = 47.61 km/h

distance between two cities is the total distance which is 89.5 km

We start with the most basic kinematic equation: distance = average speed X time traveled. In math talk, that's S = Vavg T using the standard SUVAT notation. S is the total distance traveled and T is the total time to travel that distance.