A goods truck leaves a town and travels at a constant unknown speed. Six hours later, a second truck leaves the same town in the same direction at 90 km/h. If the second truck catches up with the goods truck after 4 hours of its own journey, what is the speed of the goods truck in km/h?

Introduction / Context:
This problem is a classic example of a relative speed and catch up situation. One vehicle starts first at an unknown speed, and a faster vehicle starts later and eventually catches up. Such questions are frequently used in aptitude tests to check the understanding of distance equals speed multiplied by time and how to handle different starting times.

Given Data / Assumptions:

• The goods truck starts from a town at time zero and travels at a constant speed v km/h.
• The second truck starts 6 hours later from the same point.
• The speed of the second truck is 90 km/h.
• The second truck catches up with the goods truck after 4 hours of its own travel.
• Both trucks move in the same direction along the same route.

Concept / Approach:
When one vehicle catches another, the distances traveled by both vehicles from the starting point are the same at the moment of catching up. Therefore, we can equate the distance expressions of both trucks. The goods truck has more travel time, while the chasing truck has a higher speed. The equation distance = speed * time is used for both, and we solve for the unknown speed v of the goods truck.

Step-by-Step Solution:
Let v be the speed of the goods truck in km/h. Time traveled by goods truck when caught = 6 + 4 = 10 hours. Distance traveled by goods truck = v * 10 km. Time traveled by faster truck = 4 hours. Distance traveled by faster truck = 90 * 4 = 360 km. At catch up, distances are equal, so v * 10 = 360. Solve for v: v = 360 / 10 = 36 km/h.

Verification / Alternative check:
We can verify the answer by simulating the motion. The goods truck travels for 10 hours at 36 km/h, so distance = 36 * 10 = 360 km. The faster truck travels 4 hours at 90 km/h, also covering 360 km. Since both distances are equal, the catch up condition is satisfied, which confirms that the speed of the goods truck is indeed 36 km/h.

Why Other Options Are Wrong:
Speeds like 32 km/h, 28 km/h, 34 km/h, and 40 km/h do not satisfy the equality of distances at the catch up time. If we substitute any of these values into distance = speed * time for the goods truck, the resulting distance would not be 360 km after 10 hours, and the trucks would not meet at the same position after the given times. Therefore, these options are incorrect.

Common Pitfalls:
A common mistake is using the relative speed directly (90 - v) without accounting properly for the 6 hour head start, or forgetting to add the initial 6 hours to the goods truck travel time. Another frequent error is to assume equal times instead of equal distances at the moment of meeting. Always remember that at the catch up point, distances from the starting location are equal for both vehicles.

Final Answer:
The speed of the goods truck is 36 km/h.