A train covers 325 km in 3.5 hours on one journey and 470 km in 4 hours on another journey. What is the average speed (in km/h) of the train for the combined 795 km?

Introduction / Context:
This question checks your understanding of average speed over multiple segments where distances and times differ. Average speed is not the simple average of two speeds but rather the total distance divided by the total time taken. This is a very common trap in aptitude tests, so carefully aggregating distances and times is important.

Given Data / Assumptions:

• Distance in first journey = 325 km, time = 3.5 hours.
• Distance in second journey = 470 km, time = 4 hours.
• Total distance is the sum of both segments.
• Train speed on each segment is constant but may differ between segments.

Concept / Approach:
Average speed for a complete trip with varying speeds is defined as total distance divided by total time. Therefore, we add the distances and add the times, then divide. We do not average individual segment speeds directly, because each speed applies over a different distance or time.

Step-by-Step Solution:
First distance = 325 km. Second distance = 470 km. Total distance = 325 + 470 = 795 km. First time = 3.5 hours. Second time = 4 hours. Total time = 3.5 + 4 = 7.5 hours. Average speed = total distance / total time. Average speed = 795 / 7.5 = 106 km/h.

Verification / Alternative check:
We can observe that 7.5 * 100 = 750, so 7.5 * 106 = 795, confirming that dividing 795 by 7.5 correctly gives 106. This confirms that the average speed value is consistent.

Why Other Options Are Wrong:

• 107 km/h is slightly higher than the correct value and does not satisfy distance = average speed * total time.
• 72 km/h and 76 km/h are much lower than what is consistent with covering 795 km in only 7.5 hours.

Common Pitfalls:
Many candidates average the individual speeds of each leg instead of using total distance and total time. Others may incorrectly handle the 3.5 hour representation, forgetting that 3.5 means three and a half hours, not three hours and fifty minutes. Being precise with decimal hours and the definition of average speed prevents such mistakes.

Final Answer:
The average speed of the train for the combined journey is 106 km/h.