Ethan jogged at the swimming pool once every 2 days. Julian jogged at the same swimming pool once every 7 days. They met on 8 May 2021. There are 31 days in May and 30 days in June.
- On which date they next met each other at the swimming pool? Give your answer at the following format. (Eg 1 Jan 2000)
- How many times did they meet at the swimming pool at May and June 2021?
(a)
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Multiples of 7: 7, 14
LCM of 2 and 7: 14
Ethan and Julian met every 14 days.
14 days after 8 May 2021 = 22 May 2021
The day that they next met at the swimming pool = 22 May 2021
(b)
Since Ethan and Julian first met on 8 May 2021, they did not meet for the first 7 days of May 2021.
Total number of days from 8 May 2021 to 30 June 2021
= 31 + 30 - 7
= 54
Number of sets of 14 days from 8 May to 30 June 2021
= 54 ÷ 14
= 3 r 12
On the first day of each of the 3 sets of 14 days, they would meet at the swimming pool.
Since there is a remainder of 12, this means that on the first day of the remaining 12 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in May 2021 and June 2021
= 3 + 1
= 4
Answer(s): (a) 22 May 2021; (b) 4
