Rajesh rows a boat in still water at a speed of 4.5 km/h to go to a certain place and return. If the river flows at 1.5 km/h, what is his average speed for the entire round trip?

Introduction / Context:
Average speed in a round trip with different speeds in each direction is a common concept tested in aptitude exams. This boat and stream version requires you to compute effective downstream and upstream speeds first and then use total distance and total time to find the true average speed for the whole journey.

Given Data / Assumptions:
- Speed of Rajesh in still water = 4.5 km/h. - Speed of river current = 1.5 km/h. - Let distance to the place (one way) be d km. - Downstream speed = 4.5 + 1.5 km/h. - Upstream speed = 4.5 - 1.5 km/h.

Concept / Approach:
Average speed for a trip is defined as total distance divided by total time. Because the speeds downstream and upstream differ, we cannot simply average the two speeds. Instead, we compute the time taken for downstream and upstream separately using time = distance / speed, then add them, and finally divide the total distance 2d by the total time to get the average speed.

Step-by-Step Solution:
Step 1: Downstream speed = 4.5 + 1.5 = 6 km/h. Step 2: Upstream speed = 4.5 - 1.5 = 3 km/h. Step 3: Time taken downstream = d / 6 hours. Step 4: Time taken upstream = d / 3 hours. Step 5: Total distance for the round trip = d (going) + d (returning) = 2d. Step 6: Total time T = d / 6 + d / 3. Step 7: Simplify T: d / 6 + d / 3 = d / 6 + 2d / 6 = 3d / 6 = d / 2 hours. Step 8: Average speed = total distance / total time = 2d / (d / 2). Step 9: 2d divided by (d / 2) = 2d * (2 / d) = 4 km/h.

Verification / Alternative check:
Choose a convenient distance, say d = 6 km. Then downstream time = 6 / 6 = 1 hour; upstream time = 6 / 3 = 2 hours. Total distance = 12 km, total time = 3 hours. Average speed = 12 / 3 = 4 km/h. This specific example confirms the general calculation.

Why Other Options Are Wrong:
- 2 km/h and 8 km/h are far from the speeds involved and do not reflect correct averaging. - 6 km/h simply repeats the downstream speed and ignores the slower upstream leg. - 4.5 km/h is the still water speed, not the effective average when current affects both directions differently.

Common Pitfalls:
Many learners incorrectly average the downstream and upstream speeds, giving (6 + 3) / 2 = 4.5 km/h. This is wrong because average speed must always be computed as total distance divided by total time, especially when distances are same but speeds differ. Always calculate times first to avoid this mistake.

Final Answer:
Rajesh average speed for the whole journey is 4 km/h.