A plane flies along the four sides of a square field, covering each side at different constant speeds of 200 km/h, 400 km/h, 600 km/h, and 800 km/h, respectively (same side length on each leg). What is the plane’s average speed for the entire trip around the square?

Introduction / Context:Average speed for a journey with different speeds depends on whether equal distances or equal times are traveled. When the distances of segments are equal (as on a square with equal sides), the correct average is the harmonic-mean type computed by total distance divided by total time.

Given Data / Assumptions:

• Four legs of equal length L (square perimeter = 4L).
• Speeds on successive legs: 200 km/h, 400 km/h, 600 km/h, 800 km/h.
• Speed on each leg is constant.

Concept / Approach:For equal distances d at speeds v1, v2, ..., vn, average speed V = (n*d) / (d/v1 + d/v2 + ... + d/vn) = n / (1/v1 + ... + 1/vn). Here n = 4.

Step-by-Step Solution:

Verification / Alternative check:Using symbolic fractions: V = 4 / (1/200 + 1/400 + 1/600 + 1/800) = 384 exactly, confirming the decimal computation.

Why Other Options Are Wrong:

• 400 km/h and 414 km/h: These exceed the correct harmonic-mean result given the slow 200 km/h leg.
• 394 km/h and 372 km/h: Nearby distractors, but they do not match the exact reciprocal-sum calculation.

Common Pitfalls:Using the arithmetic mean instead of total distance over total time; averaging the four speeds directly is incorrect for equal-distance segments.

Final Answer:384 km/h