From this proportion of days he does the activities, sometimes they will meet in one day.
He will do both in the same day when the day is a common factor of 3 and 4.
Since today he did both, the next time he will do so will be in the least common factor of 3 and 4.
To get the least common factor of these, we can identify the divisors of each and makes the divisions until both get to 1. If one of the divisiors is divisior for both, we don't repeat it.
So, from 3 and 4, we can start by the divisior of 2. 2 Is a divisior of 4, but not of 3, so we divide only the number for:
3, 4 | 2
3, 2 |
Now, we have 3 and 2, so we can divide for 2 again:
3, 4 | 2
3, 2 | 2
3, 1 |
Now, we have 3 and 1, so we can only divide by 3 now:
3, 4 | 2
3, 2 | 2
3, 1 | 3
1 , 1 |
So, in the end we have 2, 2 and 3, so the least common factor is 2*2*3 = 12.
Since the common factor of 3 and 4 is 12, Tyler will lift and jog on the same day 12 days after today.