Final answer:
To find the average speed for the entire journey, we calculate the total distance traveled and the total time taken. The correct average speed for the journey is 54 km/hr.
Step-by-step explanation:
To find the average speed for the entire journey, we need to calculate the total distance traveled and the total time taken. In this case, the person covers three stretches of the same length at speeds of 30 km/hr, 60 km/hr, and 90 km/hr, respectively.
Let's say the length of each stretch is 'd' km. Since the person covers three stretches, the total distance traveled is 3d km.
The time taken to cover each stretch will be 'd/30', 'd/60', and 'd/90' hours, respectively. So, the total time taken is (d/30) + (d/60) + (d/90) hours.
Now, we can calculate the average speed using the formula:
Average speed = Total distance / Total time
Average speed = (3d) / ((d/30) + (d/60) + (d/90))
Simplifying this expression, we get:
Average speed = 54 km/hr
Therefore, the correct option is (b) 54 km/hr.