A man covers a total distance of 100 km on a bicycle. For the first 2 hours he rides at 20 km/h and for the remaining journey he rides at 10 km/h. What is his average speed for the whole journey in km/h?

Introduction / Context:

This problem tests your understanding of the concept of average speed when different parts of a journey are travelled at different speeds. Many students mistakenly take the simple average of the given speeds, but that is not correct unless the times or distances satisfy specific conditions. Here, the man rides at one speed for a fixed time and then switches to a different speed for the rest of the distance. We must compute the total time and then use the definition of average speed.

Given Data / Assumptions:

• Total distance covered = 100 km.
• Speed for the first part of the trip = 20 km/h.
• Duration of the first part = 2 hours.
• Speed for the remaining distance = 10 km/h.
• Motion is uniform at each stated speed and there are no breaks.

Concept / Approach:

The average speed for the entire journey is defined as total distance divided by total time. We first compute how much distance is covered in the first 2 hours at 20 km/h. The remaining distance is then covered at 10 km/h. From this we calculate the time taken for the second part, add both times to obtain total time, and finally divide the total distance of 100 km by the total time. This correct approach avoids the mistake of simply averaging the two speeds.

Step-by-Step Solution:

Verification / Alternative check:

We can double check by thinking about the relative contributions of the speeds. The man spends only 2 hours at the higher speed and as many as 6 hours at the lower speed. Therefore the average speed must be much closer to 10 km/h than to 20 km/h. A value like 12.5 km/h is reasonable. If we had simply averaged 20 and 10 to get 15 km/h, that would ignore the fact that he spent more time at the slower speed, which would not make sense.

Why Other Options Are Wrong:

Option 13 km/h is too high given that most of the time is at 10 km/h. Option 15.5 km/h and 20 km/h are even more unrealistic because they imply that the slow part has little influence, which is not true. Only 12.5 km/h matches the calculation based on total distance and total time, making it the correct average speed for the complete trip.

Common Pitfalls:

A very common mistake is to take the simple arithmetic mean of the two speeds without considering how long each speed was maintained. Another error is to forget that total distance is fixed at 100 km and assume equal distances for each speed, which is not given. Learners may also miscalculate the remaining distance or forget to convert all quantities into consistent units before performing the calculations.

Final Answer:

The average speed of the man for the entire bicycle journey is 12.5 km/h.