Julian jogged at the park once every 6 days. Oliver jogged at the same park once every 8 days. They met on 7 June 2009. There are 30 days in June and 31 days in July.
- On which date they next met each other at the park? Give your answer at the following format. (Eg 1 Jan 2000)
- How many times did they meet at the park at June and July 2009?
(a)
Multiples of 6: 6, 12, 18, 24
Multiples of 8: 8, 16, 24
LCM of 6 and 8: 24
Julian and Oliver met every 24 days.
24 days after 7 June 2009 = 31 Jun 2009
The day that they next met at the park = 31 Jun 2009
(b)
Since Julian and Oliver first met on 7 June 2009, they did not meet for the first 6 days of June 2009.
Total number of days from 7 June 2009 to 30 July 2009
= 30 + 31 - 6
= 55
Number of sets of 24 days from 7 June to 30 July 2009
= 55 ÷ 24
= 2 r 7
On the first day of each of the 2 sets of 24 days, they would meet at the park.
Since there is a remainder of 7, this means that on the first day of the remaining 7 days, they would meet at the park again.
Number of times that they met at the park in June 2009 and July 2009
= 2 + 1
= 3
Answer(s): (a) 31 Jun 2009; (b) 3
