Multiple choice

A boy goes to a place with a speed of $a> km/h$ and comes back with a speed of $b> km/h$. The constant speed with which he should travel to cover the entire distance in the same total time is

  1. $\displaystyle \displaystyle \frac{a+b}{2}\>km/h$
  2. $\displaystyle \sqrt{ab}\>km/h$
  3. $\displaystyle \frac{2ab}{a+b}\>km/h$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed for equal distances is the harmonic mean of the two speeds: 2ab / (a+b).

AI explanation

Let the one-way distance be D km, making the total distance 2D km. The total time taken for the round trip is the sum of the individual times, T = D/a + D/b = D(a+b)/ab. Using the formula Speed = Distance / Time, the required constant speed is 2D / T. Substituting the expression for T gives the constant speed as 2D / [D(a+b)/ab], which simplifies to 2ab/(a+b) km/h.

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