Two cars travel from city A to city B along the same route at speeds of 60 km/h and 108 km/h respectively. One of the cars takes exactly 2 hours less time than the other to complete the journey. What is the distance (in kilometres) between city A and city B?

Introduction / Context:
This problem is another example of comparing travel times for two vehicles moving over the same distance but at different constant speeds. The key is to interpret the statement about one car taking 2 hours less than the other as a precise relationship between their times and to translate that into an equation involving the unknown distance.

Given Data / Assumptions:

Speed of the slower car = 60 km/h.
Speed of the faster car = 108 km/h.
Both cars cover the same distance between city A and city B.
The faster car takes 2 hours less time than the slower car.
Speeds remain constant during the journey and there are no breaks.
We need to find the distance between the two cities.

Concept / Approach:
If D is the distance, time taken by the slower car is D / 60 hours and time taken by the faster car is D / 108 hours. The time difference between them is D / 60 − D / 108, which is given to be 2 hours. By setting up and solving the equation D / 60 − D / 108 = 2, we can determine the value of D. This approach uses basic algebra and the fundamental distance speed time relationship.

Step-by-Step Solution:
Step 1: Let the common distance between city A and city B be D kilometres. Step 2: Time taken by the slower car (60 km/h) = D / 60 hours. Step 3: Time taken by the faster car (108 km/h) = D / 108 hours. Step 4: The faster car takes 2 hours less, so D / 60 − D / 108 = 2. Step 5: Compute the difference in fractions: 1 / 60 − 1 / 108 = (108 − 60) / (60 * 108) = 48 / 6480 = 1 / 135. Step 6: So D * (1 / 135) = 2, hence D = 2 * 135 = 270 kilometres. Step 7: Therefore, the distance between the two cities is 270 km.

Verification / Alternative check:
For D = 270 km, time for the slower car is 270 / 60 = 4.5 hours and time for the faster car is 270 / 108 = 2.5 hours. The difference is 4.5 − 2.5 = 2 hours, which matches the given information. Thus, the computed distance is correct.

Why Other Options Are Wrong:
If the distance were 324 km, times would be 5.4 and 3 hours, giving a difference of 2.4 hours. For 405 km, the difference would be even larger, not 2 hours. Distances like 216 km or 300 km also lead to time differences that are not equal to 2 hours. Only 270 km yields the exact 2 hour difference required by the problem statement.

Common Pitfalls:
Some learners attempt to guess the distance or directly manipulate speeds without forming the time difference equation. Others miscompute the fraction 1 / 60 − 1 / 108 or forget whether the faster car time should be subtracted from the slower car time or the reverse. Writing the relationship carefully and systematically solving the equation avoids these errors.

Final Answer:
The distance between city A and city B is 270 kilometres.