Luis jogged at the swimming pool once every 4 days. Caden jogged at the same swimming pool once every 6 days. They met on 7 June 2016. There are 30 days in June and 31 days in July.
- 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 June and July 2016?
(a)
Multiples of 4: 4, 8, 12
Multiples of 6: 6, 12
LCM of 4 and 6: 12
Luis and Caden met every 12 days.
12 days after 7 June 2016 = 19 Jun 2016
The day that they next met at the swimming pool = 19 Jun 2016
(b)
Since Luis and Caden first met on 7 June 2016, they did not meet for the first 6 days of June 2016.
Total number of days from 7 June 2016 to 30 July 2016
= 30 + 31 - 6
= 55
Number of sets of 12 days from 7 June to 30 July 2016
= 55 ÷ 12
= 4 r 7
On the first day of each of the 4 sets of 12 days, they would meet at the swimming pool.
Since there is a remainder of 7, this means that on the first day of the remaining 7 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in June 2016 and July 2016
= 4 + 1
= 5
Answer(s): (a) 19 Jun 2016; (b) 5
