A boat travels upstream at a speed of 24 km/h and returns downstream over the same distance at a speed of 40 km/h. What is the average speed (in km/h) for the entire round trip (going and coming back over equal distances)?

Introduction / Context:
This problem tests the concept of average speed over a round trip when the distances in the two legs are equal but the speeds are different. A very common trap is to take the simple arithmetic mean of the two speeds, but that is incorrect for equal-distance travel. The correct method is to use total distance divided by total time, which naturally leads to the harmonic mean for two equal distances.

Given Data / Assumptions:

• Upstream speed = 24 km/h
• Downstream speed = 40 km/h
• The boat returns over the same distance (equal distances each way)
• Let one-way distance = d km
• We must find the average speed for the full journey

Concept / Approach:
Average speed is defined as: Average speed = (total distance) / (total time) Here the total distance is: d + d = 2d Time taken upstream is: t1 = d / 24 Time taken downstream is: t2 = d / 40 So total time is: t1 + t2 = d/24 + d/40 Then: Average speed = 2d / (d/24 + d/40) The d cancels, so we get a clean numeric answer without needing the actual distance.

Step-by-Step Solution:
Step 1: Let the one-way distance be d km. Step 2: Write the times for each leg. Upstream time = d / 24 Downstream time = d / 40 Step 3: Write total distance and total time. Total distance = 2d Total time = d/24 + d/40 Step 4: Compute average speed. Average speed = 2d / (d/24 + d/40) = 2d / (d * (1/24 + 1/40)) = 2 / (1/24 + 1/40) Step 5: Add the fractions. 1/24 + 1/40 = (40 + 24) / (24 * 40) = 64 / 960 = 1 / 15 Step 6: Finish the calculation. Average speed = 2 / (1/15) = 2 * 15 = 30
Verification / Alternative check:
Pick an easy distance, say d = 120 km. Upstream time = 120/24 = 5 hours. Downstream time = 120/40 = 3 hours. Total distance = 240 km, total time = 8 hours. Average speed = 240/8 = 30 km/h, confirming the result.
Why Other Options Are Wrong:
32 is the simple average (24 + 40) / 2, which is incorrect because time spent at 24 km/h is longer than time spent at 40 km/h. 31 and 33 are near the wrong arithmetic mean idea and do not match total distance divided by total time. 28 would imply even more time than the upstream leg justifies, and does not satisfy the equal-distance condition when verified with any sample distance.
Common Pitfalls:
The biggest mistake is using arithmetic mean for equal distances. For equal distances, you must use total distance / total time, which becomes the harmonic mean. Another mistake is assuming the distance matters; in equal-distance two-speed problems, distance cancels out if set up correctly.
Final Answer:
The average speed for the full round trip is 30 km/h.