Multiple choice

A man travels the first part of his journey at $20$ km/hr and the next at $70$ km/h, covering the entire journey at an average speed of $50 $km/h. What is the ratio of the distance that the covered at $20$ km/h to that he covered at $70 $km/h?

  1. $4:21$
  2. $3:22$
  3. $1:4$
  4. $3:5$
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A Correct answer
Explanation

Let distances be d1 and d2. Average speed = Total Distance / Total Time = (d1+d2) / (d1/20 + d2/70) = 50. (d1+d2) / ((7d1+2d2)/140) = 50. 140(d1+d2) = 50(7d1+2d2). 14d1 + 14d2 = 35d1 + 10d2. 4d2 = 21d1. d1/d2 = 4/21.

AI explanation

Since equal average speeds are not given, assume the first distance is d1 and the second is d2. The total time equals d1/20 + d2/70, and the average speed formula gives 50 = (d1 + d2) / (d1/20 + d2/70). Cross-multiplying yields 50(d1/20 + d2/70) = d1 + d2, which simplifies to 2.5d1 + 5d2/7 = d1 + d2. Subtracting d1 and d2 from both sides gives 1.5d1 = 2d2/7, so the ratio d1/d2 = (2/7) / 1.5 = 4/21. Therefore, the ratio of the distances is 4:21.

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