the people walk in a circular path. the first person finishes in 9 minutes and the second finishes in 12 minutes. How many minutes will it take till the two people meet at the start of the circle at the same time?

Question

anonymous · Answer

am I correct in saying 46 minutes?

anonymous · Answer

Hmm. i think that is the wrong answer.

It would be better if you explain how you got your answer so we can point out the mistakes.

Anyway, here is how i will approach the question.

The first person finish walking the circle in 9 minutes,
The second person finish walking the circle in 12 minutes. 

To someone who is fast and used to seeing questions of this nature, the first thing that come to mind will be to find the common multiple. If you think about it, given the common multiple of 36 ( 4x9=36; 3x12=36). in 36 minutes, the first man will complete 4 rounds of the circle, while the 2nd man will complete 3 rounds of the circle, thus they will meet each other at the starting point at the same time, although completing different rounds of the circle. (Btw, 36 is the answer). 

But to think about it step by step, in 1 min, the first man travels 1/9 of the circle, while the 2nd man travels 1/12 of the circle. 

In 9 minutes, the first man complete one round, while the 2nd man is 9/12 done, which is also 3/4. so every 9 minutes, the 1st man laps the 2nd man by 1/4 of a circle. They will only meet at the starting point at the same time when the first man is ahead of the 2nd man by one round exactly. 

Since in 9 minutes, he is only 1/4 ahead. To be 4/4 ahead of the 2nd man, it will take 4x9=36mins.

anonymous · Answer

meant to type in 36 sorry for the confusion but you explanation was good