Gabriel jogged at the park once every 3 days. Ben jogged at the same park once every 5 days. They met on 4 May 2013. 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 2013?
(a)
Multiples of 3: 3, 6, 9, 12, 15
Multiples of 5: 5, 10, 15
LCM of 3 and 5: 15
Gabriel and Ben met every 15 days.
15 days after 4 May 2013 = 19 May 2013
The day that they next met at the park = 19 May 2013
(b)
Since Gabriel and Ben first met on 4 May 2013, they did not meet for the first 3 days of May 2013.
Total number of days from 4 May 2013 to 30 June 2013
= 31 + 30 - 3
= 58
Number of sets of 15 days from 4 May to 30 June 2013
= 58 ÷ 15
= 3 r 13
On the first day of each of the 3 sets of 15 days, they would meet at the park.
Since there is a remainder of 13, this means that on the first day of the remaining 13 days, they would meet at the park again.
Number of times that they met at the park in May 2013 and June 2013
= 3 + 1
= 4
Answer(s): (a) 19 May 2013; (b) 4
