Mark jogged in the stadium once every 3 days. Wesley jogged in the same stadium once every 8 days. They met on 5 September 2019. There are 30 days in September and 31 days in October.
- 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 September and October 2019?
(a)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24
Multiples of 8: 8, 16, 24
LCM of 3 and 8: 24
Mark and Wesley met every 24 days.
24 days after 5 September 2019 = 29 Sep 2019
The day that they next met in the stadium = 29 Sep 2019
(b)
Since Mark and Wesley first met on 5 September 2019, they did not meet for the first 4 days of September 2019.
Total number of days from 5 September 2019 to 30 October 2019
= 30 + 31 - 4
= 57
Number of sets of 24 days from 5 September to 30 October 2019
= 57 ÷ 24
= 2 r 9
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 9, this means that on the first day of the remaining 9 days, they would meet in the stadium again.
Number of times that they met in the stadium in September 2019 and October 2019
= 2 + 1
= 3
Answer(s): (a) 29 Sep 2019; (b) 3
