Paul jogged in the gym once every 6 days. Asher jogged in the same gym once every 8 days. They met on 5 October 2005. 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 2005?
(a)
Multiples of 6: 6, 12, 18, 24
Multiples of 8: 8, 16, 24
LCM of 6 and 8: 24
Paul and Asher met every 24 days.
24 days after 5 October 2005 = 29 Oct 2005
The day that they next met in the gym = 29 Oct 2005
(b)
Since Paul and Asher first met on 5 October 2005, they did not meet for the first 4 days of October 2005.
Total number of days from 5 October 2005 to 30 November 2005
= 31 + 30 - 4
= 57
Number of sets of 24 days from 5 October to 30 November 2005
= 57 ÷ 24
= 2 r 9
On the first day of each of the 2 sets of 24 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 2005 and November 2005
= 2 + 1
= 3
Answer(s): (a) 29 Oct 2005; (b) 3
