Xavier jogged at the swimming pool once every 3 days. Justin jogged at the same swimming pool once every 7 days. They met on 6 October 2013. There are 31 days in October and 30 days in November.
- 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 October and November 2013?
(a)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 7: 7, 14, 21
LCM of 3 and 7: 21
Xavier and Justin met every 21 days.
21 days after 6 October 2013 = 27 Oct 2013
The day that they next met at the swimming pool = 27 Oct 2013
(b)
Since Xavier and Justin first met on 6 October 2013, they did not meet for the first 5 days of October 2013.
Total number of days from 6 October 2013 to 30 November 2013
= 31 + 30 - 5
= 56
Number of sets of 21 days from 6 October to 30 November 2013
= 56 ÷ 21
= 2 r 14
On the first day of each of the 2 sets of 21 days, they would meet at the swimming pool.
Since there is a remainder of 14, this means that on the first day of the remaining 14 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in October 2013 and November 2013
= 2 + 1
= 3
Answer(s): (a) 27 Oct 2013; (b) 3
