Two different trains each cover the same distance of 180 km. The first train takes 5 hours, while the second train takes 1 hour less. If both trains are moving in the same direction, what is the difference between the distances they each cover in one hour?

Introduction / Context:
This question tests the basic relation between distance, speed, and time, and specifically focuses on interpreting speed as the distance covered in one hour. By comparing two trains that cover the same total distance in different times, we can directly compare their speeds and hence the distance each covers per hour. This type of problem is common in aptitude tests because it checks both conceptual understanding and quick calculation skills.

Given Data / Assumptions:

• Distance covered by each train = 180 km.
• Train 1 takes 5 hours to cover 180 km.
• Train 2 takes 1 hour less, so it takes 4 hours to cover 180 km.
• We need the difference in distance covered by the two trains in one hour.
• Both trains are assumed to move at constant speeds.

Concept / Approach:
Speed is defined as distance divided by time. When the total distance is fixed and time changes, the speed changes accordingly. Since the question asks about the distances covered in one hour, we first calculate the speed of each train in km/h and then subtract the smaller speed from the larger speed. The result directly gives the required difference in distance covered in one hour because distance in one hour equals speed in km/h.

Step-by-Step Solution:
Speed of Train 1 = distance / time = 180 / 5 km/h Speed of Train 1 = 36 km/h Speed of Train 2 = distance / time = 180 / 4 km/h Speed of Train 2 = 45 km/h Difference in speeds = 45 - 36 km/h Difference in speeds = 9 km/h Since speed in km/h equals distance traveled in one hour, the difference in distance covered in one hour is 9 km.

Verification / Alternative check:
As a quick check, imagine observing both trains for exactly 1 hour. In that time, Train 1 will go 36 km, and Train 2 will go 45 km. The gap between them would then be 45 - 36 = 9 km. This matches our previous calculation and confirms that the answer is correct. Using simple mental arithmetic or checking by ratio of times also leads to the same result.

Why Other Options Are Wrong:
15 km and 18 km correspond to much larger speed differences than those produced by changing the travel time from 5 hours to 4 hours for a 180 km journey. The value 6 km is too small and does not match the correct difference in speeds. The option 12 km also arises from incorrect manipulation of the ratio or distance and time values. Only 9 km matches the correct calculation.

Common Pitfalls:
Many students mistakenly subtract the times (5 hours and 4 hours) and misinterpret that difference directly as a distance. Others compute average speeds incorrectly by mixing up the formulas or doing mental math too quickly. Carefully applying the formula speed = distance / time and then interpreting speed as distance in one hour helps avoid such errors.

Final Answer:
The difference in distance covered by the two trains in one hour is 9 km.