Oliver jogged in the stadium once every 3 days. Sam jogged in the same stadium once every 7 days. They met on 8 April 2022. There are 30 days in April and 31 days in May.
- 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 April and May 2022?
(a)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 7: 7, 14, 21
LCM of 3 and 7: 21
Oliver and Sam met every 21 days.
21 days after 8 April 2022 = 29 Apr 2022
The day that they next met in the stadium = 29 Apr 2022
(b)
Since Oliver and Sam first met on 8 April 2022, they did not meet for the first 7 days of April 2022.
Total number of days from 8 April 2022 to 30 May 2022
= 30 + 31 - 7
= 54
Number of sets of 21 days from 8 April to 30 May 2022
= 54 ÷ 21
= 2 r 12
On the first day of each of the 2 sets of 21 days, they would meet in the stadium.
Since there is a remainder of 12, this means that on the first day of the remaining 12 days, they would meet in the stadium again.
Number of times that they met in the stadium in April 2022 and May 2022
= 2 + 1
= 3
Answer(s): (a) 29 Apr 2022; (b) 3
