Multiple choice

A boy goes to school from his home at a speed of $x$ km/hr. and comes back at a speed of $y$ km/hr. then the average speed of the boy is

  1. $\displaystyle \frac{x+y}{2}km/hr$
  2. $\displaystyle \sqrt{xy}km/hr$
  3. $\displaystyle \frac{2xy}{x+y}km/hr$
  4. $\displaystyle \frac{x+y}{2xy}km/hr$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Let distance be d. Time taken to go = d/x. Time taken to return = d/y. Total time = d/x + d/y = d(x+y)/(xy). Average speed = 2d / (d(x+y)/(xy)) = 2xy / (x+y).

AI explanation

For a round trip where the boy travels equal distances to and from school at two different speeds, the average speed is calculated using the harmonic mean formula. The formula is 2 times the first speed multiplied by the second speed, divided by the sum of the two speeds. Substituting the given speeds x and y into the formula, we get 2 times x times y divided by x plus y. The average speed of the boy is 2xy divided by x plus y km/hr.

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