Pierre jogged in the stadium once every 6 days. Michael jogged in the same stadium once every 8 days. They met on 7 June 2022. There are 30 days in June and 31 days in July.
- On which date they next met each other in the stadium? Give your answer in the following format. (Eg 1 Jan 2000)
- How many times did they meet in the stadium in June and July 2022?
(a)
Multiples of 6: 6, 12, 18, 24
Multiples of 8: 8, 16, 24
LCM of 6 and 8: 24
Pierre and Michael met every 24 days.
24 days after 7 June 2022 = 31 Jun 2022
The day that they next met in the stadium = 31 Jun 2022
(b)
Since Pierre and Michael first met on 7 June 2022, they did not meet for the first 6 days of June 2022.
Total number of days from 7 June 2022 to 30 July 2022
= 30 + 31 - 6
= 55
Number of sets of 24 days from 7 June to 30 July 2022
= 55 ÷ 24
= 2 r 7
On the first day of each of the 2 sets of 24 days, they would meet in the stadium.
Since there is a remainder of 7, this means that on the first day of the remaining 7 days, they would meet in the stadium again.
Number of times that they met in the stadium in June 2022 and July 2022
= 2 + 1
= 3
Answer(s): (a) 31 Jun 2022; (b) 3
