Final answer:
Kim will complete both swimming and jogging on the same day again in 30 days, as 30 is the least common multiple of the intervals of 6 and 10 days for each activity respectively.
Step-by-step explanation:
To find out when Kim will swim and jog on the same day again, we need to calculate the least common multiple (LCM) of the two intervals: 6 days for swimming and 10 days for jogging. The LCM of 6 and 10 is the smallest number that both 6 and 10 can divide into without leaving a remainder.
- Multiple of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
- Multiple of 10: 10, 20, 30, 40, 50, 60, ...
As we can see from the lists of multiples, the smallest common multiple of 6 and 10 is 30. Therefore, Kim will complete both activities again in 30 days.