John jogged at the swimming pool once every 4 days. Ahmad jogged at the same swimming pool once every 5 days. They met on 10 October 2020. There are 31 days in October and 30 days in November.
- 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 October and November 2020?
(a)
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 5: 5, 10, 15, 20
LCM of 4 and 5: 20
John and Ahmad met every 20 days.
20 days after 10 October 2020 = 30 Oct 2020
The day that they next met at the swimming pool = 30 Oct 2020
(b)
Since John and Ahmad first met on 10 October 2020, they did not meet for the first 9 days of October 2020.
Total number of days from 10 October 2020 to 30 November 2020
= 31 + 30 - 9
= 52
Number of sets of 20 days from 10 October to 30 November 2020
= 52 ÷ 20
= 2 r 12
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 12, this means that on the first day of the remaining 12 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in October 2020 and November 2020
= 2 + 1
= 3
Answer(s): (a) 30 Oct 2020; (b) 3
