Sue can run round track 4 times in the same time it takes jack to run around the track 3 times

Question

Sue can run round track 4 times in the same time it takes jack to run around the track 3 times if they both start at the same time how many times will sue run the track before she meet jack at the starting location?

Answer 1

The simple way to look at this problem is that Jack runs at 3/4 the speed of Sue. When Sue completes her first lap, Jack is 1/4 of a lap behind her. Every time Sue completes another lap, Jack falls behind another 1/4 of a lap. So, when she completes her second lap, Jack is 1/2 a lap behind her. As Sue completes her third lap, Jack falls behind another quarter of a lap and is now 3/4 of a lap behind Sue. However, when Sue completes her fourth lap, Jack is exactly 1 lap behind her. But, this puts him right next to her again. So, when Sue completes 4 laps, she will effectively "lap" or overtake Jack, and at the starting position.