Introduction / Context:
This question is about average speed over different segments of a journey. Rakesh travels a fixed total distance, but his speed changes midway. We know his speed and time for the first part, and the total distance and total time for the entire trip. From this, we must determine the speed needed during the remaining time. This tests your ability to handle multi-stage journeys and to apply distance = speed * time correctly in each stage.
Given Data / Assumptions:
- Total distance of the journey = 368 km.
- First part: time = 5 hours, speed = 49 km/h.
- Second part: time = 3 hours, speed = unknown (let it be v km/h).
- Total time = 5 + 3 = 8 hours.
- Speeds are constant within each segment.
Concept / Approach:
We split the total distance into two parts: distance covered in the first 5 hours and distance covered in the remaining 3 hours. For each part:
distance = speed * time
The sum of these distances must equal the total distance of 368 km. We solve for the unknown speed in the second segment.
Step-by-Step Solution:
Step 1: Compute distance covered in the first 5 hours.
Speed = 49 km/h, time = 5 hours.
distance_1 = 49 * 5 = 245 km.
Step 2: Find remaining distance.
Total distance = 368 km.
distance_2 = 368 - 245 = 123 km.
Step 3: Use the time for the second part to find the speed.
Time for second part = 3 hours.
Let speed for second part be v km/h.
Then v = distance_2 / time = 123 / 3 = 41 km/h.
Therefore, Rakesh must ride at 41 km/h during the last 3 hours.
Verification / Alternative check:
We can verify by recomputing the total distance using the found speed. First part: 49 km/h * 5 h = 245 km. Second part: 41 km/h * 3 h = 123 km. Total distance = 245 + 123 = 368 km, exactly as given. The total time is still 8 hours, so the information is consistent.
Why Other Options Are Wrong:
54 km/h: Distance in last 3 hours would be 54 * 3 = 162 km, giving a total of 245 + 162 = 407 km, too large.
46 km/h: Distance in last 3 hours is 46 * 3 = 138 km, total 245 + 138 = 383 km, still too large.
58 km/h: Distance in last 3 hours is 174 km, total 245 + 174 = 419 km, much larger than 368 km.
50 km/h: Distance in last 3 hours is 150 km, total 245 + 150 = 395 km, also incorrect.
Only 41 km/h yields the exact total of 368 km.
Common Pitfalls:
Some learners mistakenly average the two speeds directly or average the times instead of dealing with distances separately. Others miscompute the distance covered in the first segment due to multiplication errors. A few may forget that the total distance must be the sum of distances from both segments, not the sum of speeds or times. Keeping each journey segment separate and applying distance = speed * time to each is the safest strategy.
Final Answer:
Rakesh must travel at
41 km/h for the remaining 3 hours of his journey.
Discussion & Comments