Riordan jogged in the gym once every 4 days. Daniel jogged in the same gym once every 5 days. They met on 9 September 2007. 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 2007?
(a)
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 5: 5, 10, 15, 20
LCM of 4 and 5: 20
Riordan and Daniel met every 20 days.
20 days after 9 September 2007 = 29 Sep 2007
The day that they next met in the gym = 29 Sep 2007
(b)
Since Riordan and Daniel first met on 9 September 2007, they did not meet for the first 8 days of September 2007.
Total number of days from 9 September 2007 to 30 October 2007
= 30 + 31 - 8
= 53
Number of sets of 20 days from 9 September to 30 October 2007
= 53 ÷ 20
= 2 r 13
On the first day of each of the 2 sets of 20 days, they would meet in the gym.
Since there is a remainder of 13, this means that on the first day of the remaining 13 days, they would meet in the gym again.
Number of times that they met in the gym in September 2007 and October 2007
= 2 + 1
= 3
Answer(s): (a) 29 Sep 2007; (b) 3
