Two cars travel from city A to city B at constant speeds of 30 km/h and 45 km/h respectively. If one car takes 2.5 hours less time than the other car to cover the whole journey, then what is the distance between city A and city B?

Introduction / Context:
This time and distance question tests your understanding of the basic relation distance = speed * time and how to set up equations when two different speeds produce a known time difference. Such problems are very common in aptitude exams as they check algebraic manipulation and interpretation of word statements.

Given Data / Assumptions:

• Car 1 speed = 30 km/h.
• Car 2 speed = 45 km/h.
• Both travel the same distance between city A and city B.
• The faster car takes 2.5 hours less than the slower car.
• We assume both move at constant speeds without breaks.

Concept / Approach:
We use the formula distance = speed * time. Since the distance is the same for both cars, we can equate the two distance expressions. The key is to represent both travel times in terms of the same unknown distance and then use the given time difference to form an equation.

Step-by-Step Solution:
Let D be the distance between city A and city B in km. Time taken by slower car (30 km/h) = D / 30 hours. Time taken by faster car (45 km/h) = D / 45 hours. Given that the faster car saves 2.5 hours: D / 30 - D / 45 = 2.5. Compute left side: 1/30 - 1/45 = (3 - 2) / 90 = 1 / 90. So (1 / 90) * D = 2.5. Therefore D = 2.5 * 90 = 225 km.
Verification / Alternative check:
Check times with D = 225 km. Time at 30 km/h = 225 / 30 = 7.5 hours. Time at 45 km/h = 225 / 45 = 5 hours. Difference = 7.5 - 5 = 2.5 hours, which matches the given condition.
Why Other Options Are Wrong:
270 km gives times 9 hours and 6 hours, difference 3 hours, not 2.5 hours. 338 km gives non simple decimal times and their difference is not 2.5 hours. 180 km gives times 6 hours and 4 hours, difference 2 hours, not 2.5 hours.
Common Pitfalls:
Students sometimes write D / 45 - D / 30 = 2.5, reversing the order of times and getting a negative value. Another mistake is to treat 2.5 as 2 hours 5 minutes instead of 2.5 hours, but here 2.5 clearly means two and a half hours. Also, using an approximate fraction for 2.5 too early can lead to rounding errors, so keep it exact as 5 / 2 if you prefer fractions.
Final Answer:
The distance between city A and city B is 225 km.