Asher jogged in the gym once every 4 days. Howard jogged in the same gym once every 6 days. They met on 3 August 2013. 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 2013?
(a)
Multiples of 4: 4, 8, 12
Multiples of 6: 6, 12
LCM of 4 and 6: 12
Asher and Howard met every 12 days.
12 days after 3 August 2013 = 15 Aug 2013
The day that they next met in the gym = 15 Aug 2013
(b)
Since Asher and Howard first met on 3 August 2013, they did not meet for the first 2 days of August 2013.
Total number of days from 3 August 2013 to 30 September 2013
= 31 + 30 - 2
= 59
Number of sets of 12 days from 3 August to 30 September 2013
= 59 ÷ 12
= 4 r 11
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 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 2013 and September 2013
= 4 + 1
= 5
Answer(s): (a) 15 Aug 2013; (b) 5
