Final answer:
The cyclist's total distance traveled was 75.2 km. At an average velocity of 24 km/h, the trip would take about 3.1 hours, which we round to 3.0 hours. This is a reasonable time for the trip, aligning with option (b).
Step-by-step explanation:
To calculate the time taken by the cyclist to complete his trip with an average velocity of 24 km/h, we first need to determine the total distance traveled. The cyclist rides 16.0 km east, 8.0 km west, 8.0 km east, 32.0 km west, and finally 11.2 km east. We can observe that the east and west movements partially cancel each other out, yet for time calculation with a given average speed, we need the sum of all distances traveled regardless of direction.
The sum of distances traveled is 16.0 km + 8.0 km + 8.0 km + 32.0 km + 11.2 km = 75.2 km.
Now, to find the time (t), we use the formula:
t = total distance / average velocity
Plugging in our numbers:
t = 75.2 km / 24 km/h = 3.133333 hours
Since we need to present the time in a sensible format, we round it to one decimal place or to the nearest multiple of 0.4 (0.4 hours equals 24 minutes, a common time unit increment), which gives us 3.1 hours or, equivalently, 3.0 hours when rounded to the options provided.
The closest option to our calculated time is (b) 3.0 hours, and this seems like a reasonable time for the trip considering the distance and average speed.