Howard jogged in the gym once every 2 days. Oliver jogged in the same gym once every 7 days. They met on 3 September 2022. 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 2022?
(a)
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Multiples of 7: 7, 14
LCM of 2 and 7: 14
Howard and Oliver met every 14 days.
14 days after 3 September 2022 = 17 Sep 2022
The day that they next met in the gym = 17 Sep 2022
(b)
Since Howard and Oliver first met on 3 September 2022, they did not meet for the first 2 days of September 2022.
Total number of days from 3 September 2022 to 30 October 2022
= 30 + 31 - 2
= 59
Number of sets of 14 days from 3 September to 30 October 2022
= 59 ÷ 14
= 4 r 3
On the first day of each of the 4 sets of 14 days, they would meet in the gym.
Since there is a remainder of 3, this means that on the first day of the remaining 3 days, they would meet in the gym again.
Number of times that they met in the gym in September 2022 and October 2022
= 4 + 1
= 5
Answer(s): (a) 17 Sep 2022; (b) 5
