Multiple choice

A car covers four successive $6km$ stretches at speeds of $25kmph$, $50kmph$, $75kmph$ and $150kmph$ respectively. Its average speed over this distance is:

  1. $25kmph$
  2. $50kmph$
  3. $75kmph$
  4. $150kmph$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 6 * 4 = 24 km. Total time = 6/25 + 6/50 + 6/75 + 6/150 = (36 + 18 + 12 + 6) / 150 = 72 / 150 = 0.48 hours. Average speed = 24 / 0.48 = 50 kmph.

AI explanation

Since the distances are equal, we use the harmonic mean formula for average speed: 4 / (1/v1 + 1/v2 + 1/v3 + 1/v4). Substituting the given speeds, we calculate 4 / (1/25 + 1/50 + 1/75 + 1/150). Finding a common denominator of 150, this becomes 4 / ((6 + 3 + 2 + 1)/150), which is 4 / (12/150). This simplifies to 4 * 150/12, resulting in an average speed of 50 kmph.