Multiple choice

A man starts from B to K, another from K to B at the same time. after passing each other they complete their journey in $\displaystyle 3\frac { 1 }{ 3 } $ and $\displaystyle 4\frac { 4 }{ 5 } $ hours respectively. Find the speed of the second man if the speed of the first is $12$ km/h ?

  1. $10 $ kmph
  2. $12$ kmph
  3. $15$ kmph
  4. $20$ kmph
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A Correct answer
Explanation

When two people meet and finish the remaining journey in times t1 and t2, the ratio of their speeds is v1/v2 = sqrt(t2/t1). Here t1 = 10/3, t2 = 24/5. v1/v2 = sqrt((24/5) / (10/3)) = sqrt(72/50) = sqrt(36/25) = 6/5. 12/v2 = 6/5, so v2 = 10 km/h.

AI explanation

According to the meeting point theorem, the ratio of the speeds of two objects is the square root of the inverse ratio of the times they take to complete their remaining journeys after crossing. This gives the ratio of their speeds as the square root of 4 and 4/5 hours divided by 3 and 1/3 hours, which is the square root of 1.44, or 1.2. If the first person's speed is 12 kmph, dividing by 1.2 yields the second person's speed of 10 kmph.

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