Solving the Aircraft Carrier Speed Problem: Average Speed to Guam

Problem: An aircraft carrier travels to Guam and back. The trip there takes 3 hours; the return takes 4 hours. The average speed for the round trip is 6 km/h. Find the average speed on the outbound leg.

Solution

Let d = one-way distance (km).

• Outbound speed = d / 3
• Return speed = d / 4
• Total distance = 2d
• Total time = 3 + 4 = 7 hours
• Round-trip average speed = Total distance / Total time = 2d / 7

Given: 2d / 7 = 6 km/h

→ 2d = 42

→ d = 21 km

Outbound speed = d / 3 = 21 / 3 = 7 km/h

Verification

• Outbound: 21 km / 3 h = 7 km/h ✓
• Return: 21 km / 4 h = 5.25 km/h
• Round-trip average: 42 km / 7 h = 6 km/h ✓

Key Concept

Average speed for a round trip ≠ arithmetic mean of the two speeds. It is the harmonic mean: 2v₁v₂ / (v₁ + v₂). Here: 2×7×5.25 / (7+5.25) = 73.5 / 12.25 = 6 km/h.