Xavier jogged in the gym once every 4 days. Flynn jogged in the same gym once every 6 days. They met on 5 October 2011. There are 31 days in October and 30 days in November.
- On which date they next met each other in the gym? Give your answer in the following format. (Eg 1 Jan 2000)
- How many times did they meet in the gym in October and November 2011?
(a)
Multiples of 4: 4, 8, 12
Multiples of 6: 6, 12
LCM of 4 and 6: 12
Xavier and Flynn met every 12 days.
12 days after 5 October 2011 = 17 Oct 2011
The day that they next met in the gym = 17 Oct 2011
(b)
Since Xavier and Flynn first met on 5 October 2011, they did not meet for the first 4 days of October 2011.
Total number of days from 5 October 2011 to 30 November 2011
= 31 + 30 - 4
= 57
Number of sets of 12 days from 5 October to 30 November 2011
= 57 ÷ 12
= 4 r 9
On the first day of each of the 4 sets of 12 days, they would meet in the gym.
Since there is a remainder of 9, this means that on the first day of the remaining 9 days, they would meet in the gym again.
Number of times that they met in the gym in October 2011 and November 2011
= 4 + 1
= 5
Answer(s): (a) 17 Oct 2011; (b) 5
