Luke jogged at the park once every 4 days. Vincent jogged at the same park once every 5 days. They met on 3 June 2012. 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 2012?
(a)
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 5: 5, 10, 15, 20
LCM of 4 and 5: 20
Luke and Vincent met every 20 days.
20 days after 3 June 2012 = 23 Jun 2012
The day that they next met at the park = 23 Jun 2012
(b)
Since Luke and Vincent first met on 3 June 2012, they did not meet for the first 2 days of June 2012.
Total number of days from 3 June 2012 to 30 July 2012
= 30 + 31 - 2
= 59
Number of sets of 20 days from 3 June to 30 July 2012
= 59 ÷ 20
= 2 r 19
On the first day of each of the 2 sets of 20 days, they would meet at the park.
Since there is a remainder of 19, this means that on the first day of the remaining 19 days, they would meet at the park again.
Number of times that they met at the park in June 2012 and July 2012
= 2 + 1
= 3
Answer(s): (a) 23 Jun 2012; (b) 3
