Answer: 12 minutes
Step-by-step explanation:
To determine when the six horses will be at the starting position again, we need to find the least common multiple (LCM) of their completion times.
Given that the completion times for the horses are 1, 2, 3, 4, and 6 minutes, we can list the multiples of each number until we find a common multiple:
Multiples of 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...
Multiples of 2: 2, 4, 6, 8, 10, 12...
Multiples of 3: 3, 6, 9, 12, ...
Multiples of 4: 4, 8, 12, ...
Multiples of 6: 6, 12, ...
Looking at the multiples, we can see that the smallest number that appears in all the lists is 12. Therefore, the horses will be at the starting position again after 12 minutes.
Hope this helped! ૮ ˶ᵔ ᵕ ᵔ˶ ა
