Two motorbikes cover the same unknown distance. One travels at 60 km/h and the other at 64 km/h. If the slower bike takes exactly 1 hour more than the faster bike, what is the distance traveled by each bike?

Introduction / Context:
This question checks the understanding of how time varies with speed when the distance is fixed. Two vehicles cover the same distance at different speeds, and the relation between their travel times is given. From this relationship, we need to determine the common distance. This is a standard kind of problem in time, speed, and distance sections of aptitude exams.

Given Data / Assumptions:

• Both motorbikes cover the same distance, say D km.
• Speed of slower bike = 60 km/h.
• Speed of faster bike = 64 km/h.
• Time taken by slower bike is 1 hour more than time taken by faster bike.
• Speeds are constant across the journey.

Concept / Approach:
We denote the time taken by each bike in hours and use the relation time = distance / speed. Since both cover the same distance, the difference in times comes only from their speeds. The problem gives the difference in times explicitly as 1 hour. Forming an equation based on this difference allows us to solve for the common distance D. This is an application of simple algebra with rational expressions.

Step-by-Step Solution:
Let D be the distance in km. Time taken by slower bike = D / 60 hours. Time taken by faster bike = D / 64 hours. Given: D / 60 = D / 64 + 1. Rearrange: D / 60 - D / 64 = 1. D * (1 / 60 - 1 / 64) = 1. 1 / 60 - 1 / 64 = (64 - 60) / (60 * 64) = 4 / 3840 = 1 / 960. So D * (1 / 960) = 1, hence D = 960 km.

Verification / Alternative check:
Check the travel times with D = 960 km. Time for slower bike = 960 / 60 = 16 hours. Time for faster bike = 960 / 64 = 15 hours. The difference is exactly 1 hour, which satisfies the condition in the problem. Therefore, 960 km is consistent with all given information.

Why Other Options Are Wrong:
For distances like 1102 km, 1060 km, 1250 km, and 840 km, the calculated times for each bike would not differ by exactly 1 hour. Substituting these values into D / 60 and D / 64 yields differences that are either less than or greater than 1 hour, so they do not satisfy the equation. Only 960 km produces the correct 1 hour difference in travel times.

Common Pitfalls:
Some students mistakenly add the speeds or try to average them instead of forming an equation using the time difference. Others might set the difference of speeds equal to the difference of times, which is incorrect. Always use time = distance / speed and set up the equation based on given time relations, then solve for distance or speed as required.

Final Answer:
The distance traveled by each motorbike is 960 km.