Ian jogged at the swimming pool once every 4 days. Daniel jogged at the same swimming pool once every 6 days. They met on 3 August 2018. There are 31 days in August and 30 days in September.
- 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 August and September 2018?
(a)
Multiples of 4: 4, 8, 12
Multiples of 6: 6, 12
LCM of 4 and 6: 12
Ian and Daniel met every 12 days.
12 days after 3 August 2018 = 15 Aug 2018
The day that they next met at the swimming pool = 15 Aug 2018
(b)
Since Ian and Daniel first met on 3 August 2018, they did not meet for the first 2 days of August 2018.
Total number of days from 3 August 2018 to 30 September 2018
= 31 + 30 - 2
= 59
Number of sets of 12 days from 3 August to 30 September 2018
= 59 ÷ 12
= 4 r 11
On the first day of each of the 4 sets of 12 days, they would meet at the swimming pool.
Since there is a remainder of 11, this means that on the first day of the remaining 11 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in August 2018 and September 2018
= 4 + 1
= 5
Answer(s): (a) 15 Aug 2018; (b) 5
