Multiple choice

A person pedals from his house to his office at a speed of $x_1$ km/hour and returns by the same route at a speed of $x_2$ km/hour. What is his average speed ?

  1. $ \displaystyle \frac {x_1x_2}{2x_1 - x_2}$
  2. $ \displaystyle \frac {x_1x_2}{x_1 + x_2}$
  3. $ \displaystyle \frac {2x_1x_2}{x_1 + x_2}$
  4. $ \displaystyle \frac {x_1x_2}{2x_1 + x_2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed is total distance divided by total time. If distance is D, time taken is D/x1 + D/x2. Average speed = 2D / (D/x1 + D/x2) = 2x1x2 / (x1 + x2).

AI explanation

When equal distances are travelled at two different speeds, the average speed is given by the harmonic mean formula: 2*x1*x2 / (x1 + x2). Multiplying the two speeds x1 and x2 by 2 yields 2*x1*x2 for the numerator. Adding the two speeds in the denominator gives x1 + x2, resulting in the average speed 2*x1*x2 / (x1 + x2).

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