Two cars travel from city A to city B, one at 42 km/h and the other at 60 km/h. If the faster car takes 2 hours less than the slower car to cover the journey, what is the distance between city A and city B?

Introduction / Context:
This time and distance problem involves two vehicles traveling the same route at different constant speeds. The key information given is the difference in time taken by each vehicle. Such questions are standard in aptitude tests and help measure your ability to translate verbal conditions into algebraic equations.

Given Data / Assumptions:
Speed of the slower car = 42 km/h.
Speed of the faster car = 60 km/h.
Both cars travel the same distance from city A to city B.
The faster car takes 2 hours less than the slower car to cover this distance.
We need to find the distance between the two cities in kilometres.

Concept / Approach:
Let the common distance be D km. Time taken by the slower car is D / 42 hours. Time taken by the faster car is D / 60 hours. The problem states that the difference in these times is 2 hours. This leads to the equation D / 42 − D / 60 = 2. Solving this equation gives the value of D. The method relies purely on the standard relationship time = distance divided by speed.

Step-by-Step Solution:
Step 1: Assume the distance between city A and city B is D km.Step 2: Time taken by slower car = D / 42 hours.Step 3: Time taken by faster car = D / 60 hours.Step 4: According to the question, D / 42 − D / 60 = 2.Step 5: Factor out D: D * (1 / 42 − 1 / 60) = 2.Step 6: Compute 1 / 42 − 1 / 60: that is (60 − 42) / (42 * 60) = 18 / 2520.Step 7: Simplify 18 / 2520 to 3 / 420 or 1 / 140.Step 8: So the equation becomes D * (1 / 140) = 2.Step 9: Therefore D = 2 * 140 = 280 km.

Verification / Alternative check:
Check the times using D = 280 km. Time for slower car = 280 / 42 = 20 / 3 hours, which is 6 hours and 40 minutes. Time for faster car = 280 / 60 = 14 / 3 hours, which is 4 hours and 40 minutes. The difference is exactly 2 hours, as stated in the problem. This confirms that the distance is correct and that the algebraic steps were carried out properly.

Why Other Options Are Wrong:
336 km, 420 km, and 224 km do not satisfy the exact 2 hour time difference when divided by the given speeds. If you plug those distances into the expressions D / 42 and D / 60, the time difference is not 2 hours.
300 km is a tempting round number, but substituting it yields times of 300 / 42 and 300 / 60, whose difference is not equal to 2 hours either.

Common Pitfalls:
One common mistake is to assume the distance is directly proportional to the difference in speeds without carefully using time. Another error is to subtract speeds instead of working with reciprocals of speeds when comparing times. Always remember that time equals distance divided by speed, so a condition on time must translate into an equation involving the reciprocals of speeds.

Final Answer:
The distance between city A and city B is 280 km.