Ryan jogged at the swimming pool once every 3 days. Riordan jogged at the same swimming pool once every 7 days. They met on 6 June 2022. There are 30 days in June and 31 days in July.
- On which date they next met each other at the swimming pool? Give your answer at the following format. (Eg 1 Jan 2000)
- How many times did they meet at the swimming pool at June and July 2022?
(a)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 7: 7, 14, 21
LCM of 3 and 7: 21
Ryan and Riordan met every 21 days.
21 days after 6 June 2022 = 27 Jun 2022
The day that they next met at the swimming pool = 27 Jun 2022
(b)
Since Ryan and Riordan first met on 6 June 2022, they did not meet for the first 5 days of June 2022.
Total number of days from 6 June 2022 to 30 July 2022
= 30 + 31 - 5
= 56
Number of sets of 21 days from 6 June to 30 July 2022
= 56 ÷ 21
= 2 r 14
On the first day of each of the 2 sets of 21 days, they would meet at the swimming pool.
Since there is a remainder of 14, this means that on the first day of the remaining 14 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in June 2022 and July 2022
= 2 + 1
= 3
Answer(s): (a) 27 Jun 2022; (b) 3
