Two cars travel from city A to city B at speeds of 36 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?

Introduction / Context:
This question is another example of comparing travel times for the same journey at different speeds. Two cars go from city A to city B, one at 36 km/h and another at 48 km/h. The faster car takes 3 hours less than the slower car. We must use this information to find the distance between the two cities. Such questions reinforce the idea that time is distance divided by speed and that differences in times can be turned into equations for the unknown distance.

Given Data / Assumptions:

• Speed of first car = 36 km/h.
• Speed of second car = 48 km/h.
• Both travel the same distance between city A and city B.
• The difference in their travel times is 3 hours.
• We assume constant speeds and a direct route.

Concept / Approach:
Let the distance between the cities be D km. Then:
time_1 = D / 36 hours. time_2 = D / 48 hours. If the slower car takes more time, the difference is:
D / 36 - D / 48 = 3. We solve this equation for D.

Step-by-Step Solution:
Step 1: Write the time difference equation. D / 36 - D / 48 = 3. Step 2: Use a common denominator for 36 and 48. The least common multiple of 36 and 48 is 144. D / 36 = (4D) / 144. D / 48 = (3D) / 144. So the equation becomes (4D / 144) - (3D / 144) = 3. This simplifies to (D / 144) = 3. Step 3: Solve for D. D = 3 * 144 = 432 km. Therefore, the distance between the two cities is 432 km.
Verification / Alternative check:
Check the times for D = 432 km:
time_1 = 432 / 36 = 12 hours. time_2 = 432 / 48 = 9 hours. Difference in times = 12 - 9 = 3 hours, which matches the given information. Thus the solution is consistent.

Why Other Options Are Wrong:
518 km, 648 km, 384 km and 346 km do not produce a time difference of exactly 3 hours when divided by 36 and 48. For example, 648 km gives 18 hours and 13.5 hours, a difference of 4.5 hours, not 3. Only 432 km produces 12 hours and 9 hours, giving the required 3-hour difference.

Common Pitfalls:
Some candidates may mistakenly add the times instead of subtracting them or may assume a wrong time difference sign. Others may choose an incorrect common denominator or make arithmetic errors when simplifying the fractions. A few may even attempt to use an average speed, which is not directly helpful here. Writing the equation carefully and checking each algebraic step prevents such mistakes.

Final Answer:
The distance between city A and city B is 432 km.