John, Louise, and Rita go swimming regularly. John goes every 2 days; Louise goes every 3 days; and Rita goes every 5 days. They all went swimming together on Friday, first day of June. When will they for swimming together?
LCM(2,3,5) = 30
so, after 30 days: Sunday, 1st of July
jhiuohi
To find out when John, Louise, and Rita will go swimming together again, we need to find the least common multiple (LCM) of their swimming intervals.
The intervals are as follows:
John = every 2 days
Louise = every 3 days
Rita = every 5 days
To find the LCM, we can list out the multiples of each interval until we find a common multiple.
John's multiples: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ...
Louise's multiples: 3, 6, 9, 12, 15, 18, 21, 24, ...
Rita's multiples: 5, 10, 15, 20, 25, 30, ...
After listing the multiples, we can see that the first common multiple is 6. Therefore, John, Louise, and Rita will go swimming together again 6 days after Friday, the first day of June.
To find the specific day of the week, we can count the days starting from Friday:
Friday (1) -> Saturday (2) -> Sunday (3) -> Monday (4) -> Tuesday (5) -> Wednesday (6)
So, they will go swimming together again on Wednesday.
To determine when John, Louise, and Rita will go swimming together again, we need to find the least common multiple (LCM) of their swimming intervals.
John goes swimming every 2 days, Louise every 3 days, and Rita every 5 days.
To find the LCM, we can follow these steps:
1. List the multiples for each person's swimming interval:
- John: 2, 4, 6, 8, 10, 12, 14, ...
- Louise: 3, 6, 9, 12, 15, 18, ...
- Rita: 5, 10, 15, 20, 25, ...
2. Identify the common multiples:
- John: 2, 4, 6, [8], 10, 12, [14], ...
- Louise: [3], [6], 9, [12], 15, [18], ...
- Rita: [5], [10], [15], 20, 25, ...
3. The common multiples are 6, 12, 18, ...
The next common multiple after 12 is 18, so they will all go swimming together on the 18th day.
Since they went swimming together on the first day of June (Friday) and the sequence of days repeats every 7 days, we can calculate the date when they will next swim together.
1st June (Friday) + 18 days = 19th June.
Therefore, John, Louise, and Rita will go swimming together again on 19th June.