Brandon jogged at the swimming pool once every 4 days. Howard jogged at the same swimming pool once every 5 days. They met on 3 April 2017. There are 30 days in April and 31 days in May.
- 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 April and May 2017?
(a)
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 5: 5, 10, 15, 20
LCM of 4 and 5: 20
Brandon and Howard met every 20 days.
20 days after 3 April 2017 = 23 Apr 2017
The day that they next met at the swimming pool = 23 Apr 2017
(b)
Since Brandon and Howard first met on 3 April 2017, they did not meet for the first 2 days of April 2017.
Total number of days from 3 April 2017 to 30 May 2017
= 30 + 31 - 2
= 59
Number of sets of 20 days from 3 April to 30 May 2017
= 59 ÷ 20
= 2 r 19
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 19, this means that on the first day of the remaining 19 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in April 2017 and May 2017
= 2 + 1
= 3
Answer(s): (a) 23 Apr 2017; (b) 3
