Two siblings, Sarah and Alex, decided to work on a fitness challenge together. They started jogging simultaneously from two different points: Sarah from Point A and Alex from Point B, which were 1 kilometre apart. Sarah jogged towards Point B, while Alex jogged towards Point A. After reaching their respective destinations, they turned around and jogged back to their starting points. This back-and-forth routine continued without any breaks. The ratio of Sarah's jogging speed to Alex's was 3 : 2. What is the total distance jogged by Sarah by the time she and Alex meet each other at Point A for the first time?

Because Sarah and Alex jog back and forth continuously between points A and B, Sarah starts at point A and Alex starts at point B. Every time Sarah reaches point A, she has completed a whole number of round trips, meaning she has been jogging for an exact multiple of her one-way travel time. During that exact same duration, Alex has also been jogging for the same amount of total time, but since his speed is slower, his travel time to reach point A is longer and will not be a whole number multiple of Sarah's round trips. Therefore, because they cannot arrive at point A at the exact same moment, they never meet at point A.

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