Brandon jogged in the gym once every 2 days. Liam jogged in the same gym once every 8 days. They met on 3 September 2014. There are 30 days in September and 31 days in October.
- 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 September and October 2014?
(a)
Multiples of 2: 2, 4, 6, 8
Multiples of 8: 8
LCM of 2 and 8: 8
Brandon and Liam met every 8 days.
8 days after 3 September 2014 = 11 Sep 2014
The day that they next met in the gym = 11 Sep 2014
(b)
Since Brandon and Liam first met on 3 September 2014, they did not meet for the first 2 days of September 2014.
Total number of days from 3 September 2014 to 30 October 2014
= 30 + 31 - 2
= 59
Number of sets of 8 days from 3 September to 30 October 2014
= 59 ÷ 8
= 7 r 3
On the first day of each of the 7 sets of 8 days, they would meet in the gym.
Since there is a remainder of 3, this means that on the first day of the remaining 3 days, they would meet in the gym again.
Number of times that they met in the gym in September 2014 and October 2014
= 7 + 1
= 8
Answer(s): (a) 11 Sep 2014; (b) 8
