Sam jogged in the stadium once every 3 days. Ethan jogged in the same stadium once every 4 days. They met on 6 May 2023. There are 31 days in May and 30 days in June.
- 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 May and June 2023?
(a)
Multiples of 3: 3, 6, 9, 12
Multiples of 4: 4, 8, 12
LCM of 3 and 4: 12
Sam and Ethan met every 12 days.
12 days after 6 May 2023 = 18 May 2023
The day that they next met in the stadium = 18 May 2023
(b)
Since Sam and Ethan first met on 6 May 2023, they did not meet for the first 5 days of May 2023.
Total number of days from 6 May 2023 to 30 June 2023
= 31 + 30 - 5
= 56
Number of sets of 12 days from 6 May to 30 June 2023
= 56 ÷ 12
= 4 r 8
On the first day of each of the 4 sets of 12 days, they would meet in the stadium.
Since there is a remainder of 8, this means that on the first day of the remaining 8 days, they would meet in the stadium again.
Number of times that they met in the stadium in May 2023 and June 2023
= 4 + 1
= 5
Answer(s): (a) 18 May 2023; (b) 5
