A boat goes a certain distance at a speed of 40 km/h and returns the same distance at a speed of 24 km/h. What is the average speed (in km/h) for the entire two-way journey?

Introduction / Context:
This is another average speed question involving a round trip with different speeds in each direction. Because the distances are the same in both directions, the correct average speed is the harmonic mean of the two speeds, not the simple arithmetic mean. Understanding this concept is essential in many aptitude tests.

Given Data / Assumptions:

• Onward journey speed = 40 km/h.
• Return journey speed = 24 km/h.
• Let the one-way distance be d km (same both ways).
• We seek the overall average speed for the round trip.

Concept / Approach:
Average speed is total distance divided by total time. For a round trip with equal distances at speeds v1 and v2, the average speed formula becomes: average speed = (2 * v1 * v2) / (v1 + v2) This is quicker than repeatedly reinventing the distance-and-time calculation but can always be derived from first principles by computing times for each leg.

Step-by-Step Solution:
Step 1: Let the one-way distance be d km. Step 2: Time taken for the first leg at 40 km/h = d / 40 hours. Step 3: Time taken for the return leg at 24 km/h = d / 24 hours. Step 4: Total distance travelled = d + d = 2d km. Step 5: Total time taken = d / 40 + d / 24. Step 6: Take the LCM of 40 and 24: 120. So d / 40 = 3d / 120 and d / 24 = 5d / 120. Step 7: Total time = (3d / 120) + (5d / 120) = 8d / 120 = d / 15 hours. Step 8: Average speed = total distance / total time = (2d) / (d / 15) = 2d * (15 / d) = 30 km/h.

Verification / Alternative check:
Using the harmonic mean formula: average speed = (2 * 40 * 24) / (40 + 24) = (1920) / 64 = 30 km/h. This matches the result above, confirming that 30 km/h is correct.

Why Other Options Are Wrong:
The arithmetic mean of 40 and 24 is 32, but this ignores that more time is spent at the lower speed. Options 28, 26 or 34 km/h do not equal total distance divided by total time when the correct speeds are used. Only 30 km/h is consistent with the travel scenario described.

Common Pitfalls:
Students frequently take the simple average of speeds, which is only valid if the times at each speed are equal, not the distances. Here, the slower speed of 24 km/h increases the time spent on that leg, pulling the average speed below 32. Always derive average speed from total distance and total time or apply the harmonic mean formula directly.

Final Answer:
The average speed for the entire journey is 30 km/h.