Two cars travel from City A to City B at constant speeds of 30 km/h and 48 km/h respectively. If one car takes 3 hours less than the other for the journey, what is the distance between City A and City B (in km)?

Introduction / Context:
This is a standard time and distance problem with two vehicles travelling the same route at different constant speeds. We are told that the faster car takes 3 hours less than the slower car to complete the journey. Using the relationship between distance, speed, and time, we can set up an equation and solve for the unknown distance between the two cities. Such questions are very common in aptitude exams and help in reinforcing algebraic modelling skills.

Given Data / Assumptions:
- Speed of slower car = 30 km/h.
- Speed of faster car = 48 km/h.
- Distance between City A and City B = D km (unknown).
- The difference in time taken by the two cars for the same distance is 3 hours.
- Both cars travel along the same straight route with constant speeds and no stops.

Concept / Approach:
The basic formula is time = distance / speed. Let the time taken by the slower car be T_s and by the faster car be T_f. Then T_s = D / 30 and T_f = D / 48. We are told that the slower car takes 3 hours more, so the time difference T_s - T_f equals 3 hours. This gives a single equation in terms of D, which can be solved easily using fractions. Once D is found, we compare it with the options provided.

Step-by-Step Solution:
Step 1: Write time expressions.Time taken by slower car = D / 30 hours.Time taken by faster car = D / 48 hours.Step 2: The slower car takes 3 hours more, so:D / 30 - D / 48 = 3.Step 3: Compute the difference in fractions.1/30 - 1/48 = (48 - 30) / (30 * 48) = 18 / 1440 = 1 / 80.Step 4: Substitute into the equation: D * (1 / 80) = 3, so D / 80 = 3.Step 5: Solve for D: D = 3 * 80 = 240 km.

Verification / Alternative check:
If the distance is 240 km, then time taken by the slower car is 240 / 30 = 8 hours, and time taken by the faster car is 240 / 48 = 5 hours. The difference in time is 8 - 5 = 3 hours, which exactly matches the condition in the problem. This confirms that the distance of 240 km is correct and consistent with all the given information.

Why Other Options Are Wrong:
- 288 km would give times of 9.6 hours and 6 hours, with a difference of 3.6 hours, not 3 hours.
- 360 km would give times of 12 hours and 7.5 hours, with a difference of 4.5 hours.
- 192 km would give times of 6.4 hours and 4 hours, with a difference of 2.4 hours.
None of these match the required 3-hour difference.

Common Pitfalls:
Students often mistakenly set up the equation with the wrong order of subtraction or forget that the slower car has the larger time. Another mistake is to attempt to average speeds instead of using the time difference condition. Being systematic about which car is slower and writing the equation as (time of slower) minus (time of faster) helps avoid sign errors. Working carefully with fractions also prevents arithmetic mistakes.

Final Answer:
The distance between City A and City B is 240 km.