Fred jogged in the gym once every 4 days. Tommy jogged in the same gym once every 5 days. They met on 9 April 2012. There are 30 days in April and 31 days in May.
- On which date they next met each other in the gym? Give your answer in the following format. (Eg 1 Jan 2000)
- How many times did they meet in the gym in April and May 2012?
(a)
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 5: 5, 10, 15, 20
LCM of 4 and 5: 20
Fred and Tommy met every 20 days.
20 days after 9 April 2012 = 29 Apr 2012
The day that they next met in the gym = 29 Apr 2012
(b)
Since Fred and Tommy first met on 9 April 2012, they did not meet for the first 8 days of April 2012.
Total number of days from 9 April 2012 to 30 May 2012
= 30 + 31 - 8
= 53
Number of sets of 20 days from 9 April to 30 May 2012
= 53 ÷ 20
= 2 r 13
On the first day of each of the 2 sets of 20 days, they would meet in the gym.
Since there is a remainder of 13, this means that on the first day of the remaining 13 days, they would meet in the gym again.
Number of times that they met in the gym in April 2012 and May 2012
= 2 + 1
= 3
Answer(s): (a) 29 Apr 2012; (b) 3
