Jagan travels from his city to another town in three stages. He covers 240 km by car at 60 km/h, then 400 km by train at 100 km/h, and finally 200 km by bus at 50 km/h. What is his average speed for the entire 840 km journey?

Introduction / Context:
This is a typical average speed problem over multiple segments of a journey, where each segment has a different speed and distance. The question tests whether students understand that average speed is total distance divided by total time, not the simple arithmetic mean of individual speeds. This concept is crucial in many quantitative reasoning problems involving journeys with varying speeds.

Given Data / Assumptions:

• Segment 1: 240 km by car at 60 km/h.
• Segment 2: 400 km by train at 100 km/h.
• Segment 3: 200 km by bus at 50 km/h.
• Total distance = 240 + 400 + 200 km.
• Speeds are constant within each segment.
• We ignore stoppage times and assume continuous travel.

Concept / Approach:
Average speed for the entire trip is defined as total distance divided by total time. We first compute the time taken for each segment using time = distance / speed, then sum these times to get total time. Once total distance and total time are known, the average speed is calculated as total distance / total time. This approach correctly weights each speed by the distance or time spent at that speed.

Step-by-Step Solution:
Total distance = 240 + 400 + 200 = 840 km. Time for car segment = 240 / 60 = 4 hours. Time for train segment = 400 / 100 = 4 hours. Time for bus segment = 200 / 50 = 4 hours. Total time = 4 + 4 + 4 = 12 hours. Average speed = total distance / total time = 840 / 12 km/h. Average speed = 70 km/h.

Verification / Alternative check:
Because each segment takes exactly 4 hours, Jagan spends equal time at speeds of 60 km/h, 100 km/h, and 50 km/h. The distance based weighted average is therefore equal to the time based weighted average. Another quick check is to multiply the average speed 70 km/h by the total time 12 hours to get 840 km, which matches the total distance, confirming the correctness of the answer.

Why Other Options Are Wrong:
Values like 72 km/h, 64 km/h, 36 km/h, or 35 km/h arise if one incorrectly averages the speeds directly or mistakenly adds and divides by the number of segments without accounting for distances and times. These do not satisfy the relationship average speed = total distance / total time for the given journey. Only 70 km/h correctly reproduces the total distance when multiplied by total time.

Common Pitfalls:
Students often incorrectly compute the average speed by simply averaging 60, 100, and 50, which gives (60 + 100 + 50) / 3 = 70 km/h in this special case, but that works here only because each segment takes the same amount of time. In general, this approach can be wrong if time segments are not equal. Remember that the definition of average speed is always total distance divided by total time.

Final Answer:
The average speed for the entire journey is 70 km/h.