Xavier jogged in the stadium once every 2 days. Henry jogged in the same stadium once every 4 days. They met on 3 June 2006. There are 30 days in June and 31 days in July.
- 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 June and July 2006?
(a)
Multiples of 2: 2, 4
Multiples of 4: 4
LCM of 2 and 4: 4
Xavier and Henry met every 4 days.
4 days after 3 June 2006 = 7 Jun 2006
The day that they next met in the stadium = 7 Jun 2006
(b)
Since Xavier and Henry first met on 3 June 2006, they did not meet for the first 2 days of June 2006.
Total number of days from 3 June 2006 to 30 July 2006
= 30 + 31 - 2
= 59
Number of sets of 4 days from 3 June to 30 July 2006
= 59 ÷ 4
= 14 r 3
On the first day of each of the 14 sets of 4 days, they would meet in the stadium.
Since there is a remainder of 3, this means that on the first day of the remaining 3 days, they would meet in the stadium again.
Number of times that they met in the stadium in June 2006 and July 2006
= 14 + 1
= 15
Answer(s): (a) 7 Jun 2006; (b) 15