Two cars start at the same time from places A and B which are 60 km apart and move in the same direction. The car from A travels at 35 km/h and the car from B travels at 25 km/h. After how many hours will the faster car catch up with the slower car?

Introduction / Context:

This question involves relative speed when two vehicles move in the same direction. Catch up problems are common in aptitude tests and help learners understand how the difference in speeds affects the time required for one object to overtake another. Here we are told that two cars start from different points 60 km apart but move in the same direction with different speeds. We must find the time it takes for the faster car to catch the slower one.

Given Data / Assumptions:

• Distance between A and B = 60 km.
• Speed of the car starting from A = 35 km/h.
• Speed of the car starting from B = 25 km/h.
• Both cars start at the same time and move in the same direction.
• We assume straight line motion with constant speeds and no stops.

Concept / Approach:

When two objects move in the same direction, the effective or relative speed between them is the difference of their speeds. The faster car reduces the gap between them at this relative speed. Time required to catch up is equal to the initial distance between them divided by the relative speed. We identify which car is faster, compute the relative speed, and then use the formula time = distance / speed.

Step-by-Step Solution:

Verification / Alternative check:

We can verify by calculating how far each car has travelled after 6 hours. In 6 hours the faster car covers 35 * 6 = 210 km. In the same time the slower car covers 25 * 6 = 150 km. The difference between these distances is 210 - 150 = 60 km, which is exactly the initial separation. Therefore after 6 hours the faster car catches up to the slower car, confirming that 6 hours is correct.

Why Other Options Are Wrong:

Option 6.5 hours would correspond to a closing distance of 10 * 6.5 = 65 km, which is more than the initial 60 km and therefore inconsistent. Option 6.2 hours and 6.52 hours likewise give closing distances that do not match the exact initial gap of 60 km. Only 6 hours gives a perfect match and satisfies the relationship between distance, time and relative speed.

Common Pitfalls:

Learners sometimes add the speeds instead of subtracting them when the vehicles are moving in the same direction, which is incorrect. Another common mistake is to mix up which car is ahead and which is behind, but the relative speed formula using the difference in speeds works regardless, as long as we use the absolute difference. It is also important to keep units consistent and to avoid guessing without using the distance divided by relative speed formula.

Final Answer:

The faster car will catch up with the slower car after 6 hours.