Riordan jogged at the park once every 3 days. Howard jogged at the same park once every 8 days. They met on 7 November 2016. There are 30 days in November and 31 days in December.
- 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 November and December 2016?
(a)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24
Multiples of 8: 8, 16, 24
LCM of 3 and 8: 24
Riordan and Howard met every 24 days.
24 days after 7 November 2016 = 31 Nov 2016
The day that they next met at the park = 31 Nov 2016
(b)
Since Riordan and Howard first met on 7 November 2016, they did not meet for the first 6 days of November 2016.
Total number of days from 7 November 2016 to 30 December 2016
= 30 + 31 - 6
= 55
Number of sets of 24 days from 7 November to 30 December 2016
= 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 November 2016 and December 2016
= 2 + 1
= 3
Answer(s): (a) 31 Nov 2016; (b) 3
