Asher jogged in the stadium once every 3 days. Valen jogged in the same stadium once every 7 days. They met on 8 November 2013. There are 30 days in November and 31 days in December.
- 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 November and December 2013?
(a)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 7: 7, 14, 21
LCM of 3 and 7: 21
Asher and Valen met every 21 days.
21 days after 8 November 2013 = 29 Nov 2013
The day that they next met in the stadium = 29 Nov 2013
(b)
Since Asher and Valen first met on 8 November 2013, they did not meet for the first 7 days of November 2013.
Total number of days from 8 November 2013 to 30 December 2013
= 30 + 31 - 7
= 54
Number of sets of 21 days from 8 November to 30 December 2013
= 54 ÷ 21
= 2 r 12
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 12, this means that on the first day of the remaining 12 days, they would meet in the stadium again.
Number of times that they met in the stadium in November 2013 and December 2013
= 2 + 1
= 3
Answer(s): (a) 29 Nov 2013; (b) 3