Two cars A and B travel from one city to another along the same route. Car A travels at 60 km/h and car B travels at 108 km/h. If car B takes exactly 2 hours less than car A to complete the journey, what is the distance (in kilometres) between the two cities?

Introduction / Context:
This problem tests relative travel times when two vehicles move over the same distance but at different constant speeds. It requires setting up an equation equating the difference in their travel times to a given value. The question is a classic example of solving for distance using the time difference between a slower and a faster vehicle.

Given Data / Assumptions:

Speed of car A = 60 km/h.
Speed of car B = 108 km/h.
Both cars travel the same distance between the two cities.
Car B takes 2 hours less than car A to cover the journey.
Speeds remain constant for the entire trip.
We need to find the common distance D in kilometres.

Concept / Approach:
If distance is D kilometres and speed is v km/h, then time taken is D / v hours. Let time taken by car A be D / 60 and time taken by car B be D / 108. We are told that the difference in their travel times is 2 hours. This gives a linear equation in D that we can solve. Once D is found, we check that the time difference matches the given value.

Step-by-Step Solution:
Step 1: Let the distance between the two cities be D kilometres. Step 2: Time taken by car A = D / 60 hours. Step 3: Time taken by car B = D / 108 hours. Step 4: According to the question, the faster car B takes 2 hours less than car A, so D / 60 − D / 108 = 2. Step 5: Compute the difference: D * (1 / 60 − 1 / 108) = 2. Step 6: Find 1 / 60 − 1 / 108 = (108 − 60) / (60 * 108) = 48 / 6480 = 1 / 135. Step 7: So D * (1 / 135) = 2, hence D = 2 * 135 = 270 kilometres.

Verification / Alternative check:
Check the times for each car. For D = 270 km, time for car A = 270 / 60 = 4.5 hours. Time for car B = 270 / 108 = 2.5 hours. The difference in time is 4.5 − 2.5 = 2 hours, which matches the given condition. Therefore, the distance between the two cities must be 270 km.

Why Other Options Are Wrong:
If D were 240 km, times would be 240 / 60 = 4 hours and 240 / 108 ≈ 2.22 hours, with a difference not equal to 2 hours. Similarly, 300 km would give times 5 hours and approximately 2.78 hours, again not differing by 2 hours. Values of 210 km or 330 km also fail to produce the correct time difference. Only 270 km satisfies the time difference of 2 hours exactly.

Common Pitfalls:
Learners sometimes mistakenly equate the ratio of speeds to the ratio of times directly or attempt to use average speeds instead of forming the proper time difference equation. Another common error is in computing the fraction 1 / 60 − 1 / 108 incorrectly. Careful algebraic manipulation and accurate fraction work prevent these mistakes.

Final Answer:
The distance between the two cities is 270 kilometres.