Tim jogged in the gym once every 3 days. Ahmad jogged in the same gym once every 7 days. They met on 9 August 2015. There are 31 days in August and 30 days in September.
- 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 August and September 2015?
(a)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 7: 7, 14, 21
LCM of 3 and 7: 21
Tim and Ahmad met every 21 days.
21 days after 9 August 2015 = 30 Aug 2015
The day that they next met in the gym = 30 Aug 2015
(b)
Since Tim and Ahmad first met on 9 August 2015, they did not meet for the first 8 days of August 2015.
Total number of days from 9 August 2015 to 30 September 2015
= 31 + 30 - 8
= 53
Number of sets of 21 days from 9 August to 30 September 2015
= 53 ÷ 21
= 2 r 11
On the first day of each of the 2 sets of 21 days, they would meet in the gym.
Since there is a remainder of 11, this means that on the first day of the remaining 11 days, they would meet in the gym again.
Number of times that they met in the gym in August 2015 and September 2015
= 2 + 1
= 3
Answer(s): (a) 30 Aug 2015; (b) 3
