Simon jogged at the swimming pool once every 4 days. Ken jogged at the same swimming pool once every 5 days. They met on 9 May 2016. There are 31 days in May and 30 days in June.
- On which date they next met each other at the swimming pool? Give your answer at the following format. (Eg 1 Jan 2000)
- How many times did they meet at the swimming pool at May and June 2016?
(a)
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 5: 5, 10, 15, 20
LCM of 4 and 5: 20
Simon and Ken met every 20 days.
20 days after 9 May 2016 = 29 May 2016
The day that they next met at the swimming pool = 29 May 2016
(b)
Since Simon and Ken first met on 9 May 2016, they did not meet for the first 8 days of May 2016.
Total number of days from 9 May 2016 to 30 June 2016
= 31 + 30 - 8
= 53
Number of sets of 20 days from 9 May to 30 June 2016
= 53 ÷ 20
= 2 r 13
On the first day of each of the 2 sets of 20 days, they would meet at the swimming pool.
Since there is a remainder of 13, this means that on the first day of the remaining 13 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in May 2016 and June 2016
= 2 + 1
= 3
Answer(s): (a) 29 May 2016; (b) 3
