Multiple choice

Tom drives around town to run errands. He travels along the four sides of a square-shaped block, with each side measuring 2 miles. Tom starts by driving at a speed of 30 miles per hour (mph), and for each subsequent side of block, he increases his speed by 10 mph until he covers all sides of the block. What is Tom's average speed during this trip?

  1. 39.20 miles per hour

  2. 41.70 miles per hour

  3. 42.10 miles per hour

  4. 46.10 miles per hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = 4 sides * 2 miles = 8 miles. Speeds are 30, 40, 50, 60 mph. Time for each side = distance / speed. T1 = 2/30 = 1/15 hr, T2 = 2/40 = 1/20 hr, T3 = 2/50 = 1/25 hr, T4 = 2/60 = 1/30 hr. Total time = (1/15 + 1/20 + 1/25 + 1/30) = (20+15+12+10)/300 = 57/300 = 19/100 hr. Average speed = Total distance / Total time = 8 / (19/100) = 800/19 = 42.105 mph.

AI explanation

Using the harmonic mean formula for average speed when equal distances are traveled at different speeds, Average Speed = 4abcd / (abc + abd + acd + bcd). Substituting the speeds of 30, 40, 50, and 60 mph gives (4 × 30 × 40 × 50 × 60) / (30 × 40 × 50 + 30 × 40 × 60 + 30 × 50 × 60 + 40 × 50 × 60). This calculates to 14400000 / 342000, resulting in an average speed of approximately 42.10 mph.

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