Raghu travels from his home to his college on a motorbike, covering a total distance of 410 kilometres during a trip. For the first 5 hours he rides at a constant speed of 50 km/h. For the remaining 4 hours he rides at a different constant speed. What is his speed (in km/h) during the remaining 4 hours of the journey?

Introduction / Context:
This question is a straightforward application of the distance speed time relationship for a journey divided into two segments with different speeds. The total distance and the time for each segment are given, and the task is to compute the unknown speed in the second segment. Such problems help reinforce the idea that total distance is the sum of segment distances and that each segment distance is speed multiplied by time.

Given Data / Assumptions:

Total distance of the trip = 410 kilometres.
Time for the first part of the journey = 5 hours.
Speed during the first part = 50 km/h.
Time for the second part of the journey = 4 hours.
Speed during the second part is constant and unknown.
There are no breaks between segments and distances simply add up.

Concept / Approach:
For each segment, distance = speed * time. The distance for the first segment can be computed directly. Let the unknown speed for the second segment be v km/h. Then its distance is v * 4. Since the sum of these two distances equals the total distance of 410 km, we set up the equation first distance + second distance = 410 and solve for v. This simple algebraic equation provides the required speed.

Step-by-Step Solution:
Step 1: Compute the distance covered in the first 5 hours. Distance_1 = speed * time = 50 * 5 = 250 kilometres. Step 2: Let the speed during the remaining 4 hours be v km/h. Step 3: Distance covered in the remaining 4 hours is Distance_2 = v * 4 kilometres. Step 4: Total distance is the sum of the two segment distances: 250 + 4v = 410. Step 5: Solve this equation for v: 4v = 410 − 250 = 160. Step 6: v = 160 / 4 = 40 km/h. Step 7: Therefore, Raghu travels at 40 km/h in the last 4 hours of his journey.

Verification / Alternative check:
Check by recomputing the total distance. First segment: 50 km/h * 5 hours = 250 km. Second segment: 40 km/h * 4 hours = 160 km. Total distance = 250 + 160 = 410 km, which matches the given total. This confirms that the computed speed of 40 km/h for the second segment is correct.

Why Other Options Are Wrong:
If Raghu rode at 47 km/h for the second part, he would cover 188 km, giving a total of 438 km. At 56 km/h, he would cover 224 km, giving 474 km total. At 48 km/h, the second part distance would be 192 km, totalling 442 km. At 52 km/h, the distance would be 208 km, totalling 458 km. None of these match the required total of 410 km. Only 40 km/h gives the correct total distance.

Common Pitfalls:
A common mistake is to average the two speeds instead of using distance and time relations or to confuse total time with time for one segment. Some learners also miscalculate the first segment distance or forget that the unknown speed must be multiplied by 4 hours, not 5. Systematically writing the equation for total distance keeps the logic clear and leads to the correct result.

Final Answer:
During the remaining 4 hours of the journey, Raghu rides at 40 km/h.