Ethan jogged in the stadium once every 3 days. Billy jogged in the same stadium once every 5 days. They met on 6 September 2022. 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 2022?
(a)
Multiples of 3: 3, 6, 9, 12, 15
Multiples of 5: 5, 10, 15
LCM of 3 and 5: 15
Ethan and Billy met every 15 days.
15 days after 6 September 2022 = 21 Sep 2022
The day that they next met in the stadium = 21 Sep 2022
(b)
Since Ethan and Billy first met on 6 September 2022, they did not meet for the first 5 days of September 2022.
Total number of days from 6 September 2022 to 30 October 2022
= 30 + 31 - 5
= 56
Number of sets of 15 days from 6 September to 30 October 2022
= 56 ÷ 15
= 3 r 11
On the first day of each of the 3 sets of 15 days, they would meet in the stadium.
Since there is a remainder of 11, this means that on the first day of the remaining 11 days, they would meet in the stadium again.
Number of times that they met in the stadium in September 2022 and October 2022
= 3 + 1
= 4
Answer(s): (a) 21 Sep 2022; (b) 4