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There is a circular path around a sports field. Sonia takes $18$ minutes to drive one round of the field, while Ravi takes $12$ minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

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Compare ratios: word problems

Full solution

Q. There is a circular path around a sports field. Sonia takes

18

minutes to drive one round of the field, while Ravi takes

12

minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Calculate LCM: Calculate the least common multiple (LCM) of Sonia's and Ravi's times to find when they will meet at the starting point. $\newline$ Sonia's time: $18$ minutes $\newline$ Ravi's time: $12$ minutes $\newline$ Find the multiples of $18$ and $12$ . $\newline$ Multiples of $18$ : $18, 36, 54, 72\ldots$ $\newline$ Multiples of $12$ : $12, 24, 36, 48\ldots$ $\newline$ The LCM of $18$ and $12$ is $12$ $0$ .
Find Multiples: The LCM is the time it will take for both Sonia and Ravi to meet at the starting point. $\newline$ So, they will meet again at the starting point after $36$ minutes.

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