Seth jogged in the stadium once every 3 days. Michael jogged in the same stadium once every 7 days. They met on 6 August 2009. There are 31 days in August and 30 days in September.
- On which date they next met each other in the stadium? Give your answer in the following format. (Eg 1 Jan 2000)
- How many times did they meet in the stadium in August and September 2009?
(a)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 7: 7, 14, 21
LCM of 3 and 7: 21
Seth and Michael met every 21 days.
21 days after 6 August 2009 = 27 Aug 2009
The day that they next met in the stadium = 27 Aug 2009
(b)
Since Seth and Michael first met on 6 August 2009, they did not meet for the first 5 days of August 2009.
Total number of days from 6 August 2009 to 30 September 2009
= 31 + 30 - 5
= 56
Number of sets of 21 days from 6 August to 30 September 2009
= 56 ÷ 21
= 2 r 14
On the first day of each of the 2 sets of 21 days, they would meet in the stadium.
Since there is a remainder of 14, this means that on the first day of the remaining 14 days, they would meet in the stadium again.
Number of times that they met in the stadium in August 2009 and September 2009
= 2 + 1
= 3
Answer(s): (a) 27 Aug 2009; (b) 3
