# 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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Given:

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.

They both start at the same point and at the same time, and go in the same direction.

To do:

We have to find the number of minutes after which they meet again at the starting point.

Solution:

Both Sonia and Ravi move in the same direction and at the same time.

Therefore,

To find the time when they will be meeting again at the starting point, we have to find LCM of 18 and 12.

This implies,

Prime factorisation of $18=2\times3\times3$

$=2\times3^2$

Prime factorisation of $12=2\times2\times3$

$=2^2\times3$

LCM $(18,12) = 2^2\times3^2$

$=36$

Hence, Sonia and Ravi will meet again at the starting point after 36 minutes.

Updated on 10-Oct-2022 13:19:30