Billy jogged at the swimming pool once every 2 days. Andy jogged at the same swimming pool once every 5 days. They met on 4 March 2014. There are 31 days in March and 30 days in April.
- 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 March and April 2014?
(a)
Multiples of 2: 2, 4, 6, 8, 10
Multiples of 5: 5, 10
LCM of 2 and 5: 10
Billy and Andy met every 10 days.
10 days after 4 March 2014 = 14 Mar 2014
The day that they next met at the swimming pool = 14 Mar 2014
(b)
Since Billy and Andy first met on 4 March 2014, they did not meet for the first 3 days of March 2014.
Total number of days from 4 March 2014 to 30 April 2014
= 31 + 30 - 3
= 58
Number of sets of 10 days from 4 March to 30 April 2014
= 58 ÷ 10
= 5 r 8
On the first day of each of the 5 sets of 10 days, they would meet at the swimming pool.
Since there is a remainder of 8, this means that on the first day of the remaining 8 days, they would meet at the swimming pool again.
Number of times that they met at the swimming pool in March 2014 and April 2014
= 5 + 1
= 6
Answer(s): (a) 14 Mar 2014; (b) 6
