Agra and Delhi are 160 km apart. A train leaves Agra for Delhi and at the same time another train leaves Delhi for Agra. The two trains meet 5 hours after they start. If the train from Agra to Delhi travels 6 km/h faster than the other train, what is the speed of the faster train?

Introduction / Context:
This is a typical meeting point problem involving two trains starting from opposite cities and moving towards each other. The question tests understanding of combined speed, distance covered before meeting, and how to use a small difference between speeds to solve for individual speeds.

Given Data / Assumptions:

• Distance between Agra and Delhi = 160 km.
• The trains start at the same time from opposite cities.
• They meet after 5 hours.
• Speed of train from Agra to Delhi is 6 km/h more than the speed of the other train.
• Both trains travel at constant speeds.

Concept / Approach:
Let the speed of the slower train be v km/h. Then the speed of the faster train is v + 6 km/h. When two trains move towards each other, the total distance covered until they meet equals the sum of the distances each train has travelled. This is also equal to (v + (v + 6)) multiplied by the time before meeting. By equating this product to the known distance, we can solve for v and then determine the faster train speed.

Step-by-Step Solution:
Let speed of slower train = v km/h. Then speed of faster train = v + 6 km/h. Time before meeting = 5 hours. Total distance covered = distance from Agra to Delhi = 160 km. So, (v + v + 6) * 5 = 160. (2v + 6) * 5 = 160 → 2v + 6 = 32 → 2v = 26 → v = 13 km/h. Speed of faster train = v + 6 = 13 + 6 = 19 km/h.

Verification / Alternative check:
At 13 km/h, the slower train travels 13 * 5 = 65 km in 5 hours. At 19 km/h, the faster train travels 19 * 5 = 95 km. The sum is 65 + 95 = 160 km, which equals the distance between the cities. Thus both the meeting time and the distance are consistent, confirming the answer.

Why Other Options Are Wrong:
Values such as 7 km/h, 9 km/h, or 13 km/h for the faster train do not satisfy the equation (v + (v + 6)) * 5 = 160. In fact, 13 km/h is the slower train speed, not the faster one. Only 19 km/h produces the correct combined distance of 160 km in 5 hours.

Common Pitfalls:
Students sometimes misinterpret which train is faster or forget to multiply by the time to get total distance. Others may assume equal speeds, which contradicts the given difference of 6 km/h. Proper variable assignment and careful equation setup help avoid these errors.

Final Answer:
The speed of the faster train is 19 km/h.