Multiple choice

David drives half the distance from $A$ to $B$ at $40$ miles per hour and the other half of the distance at $60$ miles per hour. Calculate her average rate of speed, in miles per hour, for the entire trip.

  1. 48

  2. 49

  3. 50

  4. 51

  5. 52
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A Correct answer
Explanation

The average speed for equal distances is the harmonic mean of the speeds. Using the formula 2*v1*v2 / (v1 + v2), we get 2 * 40 * 60 / (40 + 60) = 4800 / 100 = 48.

AI explanation

Since equal distances are traveled at different speeds, we use the harmonic mean formula for average speed: 2xy divided by (x plus y). Substituting the given speeds gives (2 times 40 times 60) divided by (40 plus 60). This simplifies to 4800 divided by 100, yielding an average speed of 48 miles per hour. The result is 48.

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