Ivan jogged in the gym once every 2 days. Flynn jogged in the same gym once every 8 days. They met on 7 September 2023. There are 30 days in September and 31 days in October.
- On which date they next met each other in the gym? Give your answer in the following format. (Eg 1 Jan 2000)
- How many times did they meet in the gym in September and October 2023?
(a)
Multiples of 2: 2, 4, 6, 8
Multiples of 8: 8
LCM of 2 and 8: 8
Ivan and Flynn met every 8 days.
8 days after 7 September 2023 = 15 Sep 2023
The day that they next met in the gym = 15 Sep 2023
(b)
Since Ivan and Flynn first met on 7 September 2023, they did not meet for the first 6 days of September 2023.
Total number of days from 7 September 2023 to 30 October 2023
= 30 + 31 - 6
= 55
Number of sets of 8 days from 7 September to 30 October 2023
= 55 ÷ 8
= 6 r 7
On the first day of each of the 6 sets of 8 days, they would meet in the gym.
Since there is a remainder of 7, this means that on the first day of the remaining 7 days, they would meet in the gym again.
Number of times that they met in the gym in September 2023 and October 2023
= 6 + 1
= 7
Answer(s): (a) 15 Sep 2023; (b) 7
