Multiple choice

On a 400-mile trip, Car X traveled half the distance at 40 miles per hour (mph) and the other half at 50 mph. What was the average speed of Car X?

  1. $44\cfrac{4}{9}$ mph
  2. $48$ mph
  3. $45$ mph
  4. $46$ mph
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A Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 400 miles. Time for first half = 200/40 = 5 hours. Time for second half = 200/50 = 4 hours. Total time = 9 hours. Average speed = 400/9 = 44 4/9 mph.

AI explanation

When equal distances are traveled at two different speeds, the average speed is given by the harmonic mean formula: 2ab / (a + b). Substituting the speeds 40 and 50 into the formula gives (2 * 40 * 50) / (40 + 50) = 4000 / 90. This simplifies to 400/9, which is 44 4/9 mph.

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