Sean jogged at the swimming pool once every 3 days. Eric jogged at the same swimming pool once every 8 days. They met on 5 October 2023. There are 31 days in October and 30 days in November.
- 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 October and November 2023?
(a)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24
Multiples of 8: 8, 16, 24
LCM of 3 and 8: 24
Sean and Eric met every 24 days.
24 days after 5 October 2023 = 29 Oct 2023
The day that they next met at the swimming pool = 29 Oct 2023
(b)
Since Sean and Eric first met on 5 October 2023, they did not meet for the first 4 days of October 2023.
Total number of days from 5 October 2023 to 30 November 2023
= 31 + 30 - 4
= 57
Number of sets of 24 days from 5 October to 30 November 2023
= 57 ÷ 24
= 2 r 9
On the first day of each of the 2 sets of 24 days, they would meet at the swimming pool.
Since there is a remainder of 9, this means that on the first day of the remaining 9 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in October 2023 and November 2023
= 2 + 1
= 3
Answer(s): (a) 29 Oct 2023; (b) 3
