Cody jogged at the swimming pool once every 3 days. Fabian jogged at the same swimming pool once every 5 days. They met on 8 May 2016. 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 2016?
(a)
Multiples of 3: 3, 6, 9, 12, 15
Multiples of 5: 5, 10, 15
LCM of 3 and 5: 15
Cody and Fabian met every 15 days.
15 days after 8 May 2016 = 23 May 2016
The day that they next met at the swimming pool = 23 May 2016
(b)
Since Cody and Fabian first met on 8 May 2016, they did not meet for the first 7 days of May 2016.
Total number of days from 8 May 2016 to 30 June 2016
= 31 + 30 - 7
= 54
Number of sets of 15 days from 8 May to 30 June 2016
= 54 ÷ 15
= 3 r 9
On the first day of each of the 3 sets of 15 days, they would meet at the swimming pool.
Since there is a remainder of 9, this means that on the first day of the remaining 9 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in May 2016 and June 2016
= 3 + 1
= 4
Answer(s): (a) 23 May 2016; (b) 4