To determine the average speed for the rider's entire journey, we calculate the total distance traveled and the total time taken using the formula: Average Speed = Total Distance / Total Time.

Journey Segments Speed Times

• Segment 1: The rider travels 60 km at 30 km/h.
  Time\(_1\) = \(\frac{\text{Distance}_1}{\text{Speed}_1} = \frac{60 \text{ km}}{30 \text{ km/h}} = 2 \text{ hours}\).
• Segment 2: The rider travels 40 km at 20 km/h.
  Time\(_2\) = \(\frac{\text{Distance}_2}{\text{Speed}_2} = \frac{40 \text{ km}}{20 \text{ km/h}} = 2 \text{ hours}\).
• Segment 3: The rider covers 50 km at 25 km/h.
  Time\(_3\) = \(\frac{\text{Distance}_3}{\text{Speed}_3} = \frac{50 \text{ km}}{25 \text{ km/h}} = 2 \text{ hours}\).

Total Distance and Time

Total Distance for the journey = Distance\(_1\) + Distance\(_2\) + Distance\(_3\)
Total Distance = \(60 \text{ km} + 40 \text{ km} + 50 \text{ km} = 150 \text{ km}\).

Total Time for the journey = Time\(_1\) + Time\(_2\) + Time\(_3\)
Total Time = \(2 \text{ hours} + 2 \text{ hours} + 2 \text{ hours} = 6 \text{ hours}\).

Average Speed Calculation

Now, calculate the average speed using the total distance and total time:
Average Speed = \(\frac{\text{Total Distance}}{\text{Total Time}}\)
Average Speed = \(\frac{150 \text{ km}}{6 \text{ hours}}\)
Average Speed = \(25 \text{ km/h}\).

The average speed of the rider for the entire journey is 25 km/h.