Multiple choice

A professional cyclist, Elena, is training for a cycling race and decides to test her endurance. She plans a round-trip cycling route from her home to a neighboring city and back. On her journey to the neighboring city, she cycles at an average speed of 12 miles per hour. On her return journey, she cycles at an average speed of 18 miles per hour. If the total time for the round trip is 5 hours, what is the average speed for her entire journey?

  1. 7.2 miles per hour

  2. 14.4 miles per hour

  3. 16 miles per hour

  4. 16.5 miles per hour

  5. 17 miles per hour
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the one-way distance be d. Time 1 = d/12, Time 2 = d/18. Total time = d/12 + d/18 = 5. (3d + 2d) / 36 = 5, so 5d/36 = 5, d = 36 miles. Total distance = 72 miles. Total time = 5 hours. Average speed = 72 / 5 = 14.4 mph.

AI explanation

When equal distances are traveled at different speeds, the average speed is calculated using the harmonic mean formula: 2xy / (x + y). Substituting Elena's speeds of 12 mph and 18 mph gives (2 * 12 * 18) / (12 + 18) = 432 / 30. This simplifies to an average speed of 14.4 miles per hour for the entire journey.

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