Brandon jogged at the park once every 2 days. Jeremy jogged at the same park once every 7 days. They met on 3 May 2005. There are 31 days in May and 30 days in June.
- 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 May and June 2005?
(a)
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Multiples of 7: 7, 14
LCM of 2 and 7: 14
Brandon and Jeremy met every 14 days.
14 days after 3 May 2005 = 17 May 2005
The day that they next met at the park = 17 May 2005
(b)
Since Brandon and Jeremy first met on 3 May 2005, they did not meet for the first 2 days of May 2005.
Total number of days from 3 May 2005 to 30 June 2005
= 31 + 30 - 2
= 59
Number of sets of 14 days from 3 May to 30 June 2005
= 59 ÷ 14
= 4 r 3
On the first day of each of the 4 sets of 14 days, they would meet at the park.
Since there is a remainder of 3, this means that on the first day of the remaining 3 days, they would meet at the park again.
Number of times that they met at the park in May 2005 and June 2005
= 4 + 1
= 5
Answer(s): (a) 17 May 2005; (b) 5