Anthony decided to run one mile every 5 days. John decided to run two miles every 6 days. If they both start on Saturday, April 14, when will they both run on the same day again?
To find out when Anthony and John will run on the same day again, we need to determine the common multiples of their respective running cycles.
First, let's determine the cycle for each person:
Anthony runs 1 mile every 5 days.
John runs 2 miles every 6 days.
To find the smallest common multiple, we need to find the least common multiple (LCM) of 5 and 6.
Prime factorization of 5: 5
Prime factorization of 6: 2 x 3
LCM of 5 and 6 is: 2 x 3 x 5 = 30
Therefore, Anthony and John will run on the same day again every 30 days.
Now, let's determine the starting day. They both start on Saturday, April 14.
To determine the day they will run on the same day again, we need to count the number of days after April 14. Since 30 is the cycle length, we need to find the smallest multiple of 30 that is greater than or equal to the number of days from April 14.
Let's count the days using a table:
Starting Day: Saturday, April 14
Days: 0 1 2 3 4 ... 28 29 30 31 32 ...
Dates: 14 15 16 17 18 ... 12 13 14 15 16 ...
As we can see, Anthony and John will run on the same day again on Monday, May 14, which is 30 days after Saturday, April 14.