Carl jogged in the gym once every 4 days. Bobby jogged in the same gym once every 5 days. They met on 3 October 2007. There are 31 days in October and 30 days in November.
- 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 October and November 2007?
(a)
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 5: 5, 10, 15, 20
LCM of 4 and 5: 20
Carl and Bobby met every 20 days.
20 days after 3 October 2007 = 23 Oct 2007
The day that they next met in the gym = 23 Oct 2007
(b)
Since Carl and Bobby first met on 3 October 2007, they did not meet for the first 2 days of October 2007.
Total number of days from 3 October 2007 to 30 November 2007
= 31 + 30 - 2
= 59
Number of sets of 20 days from 3 October to 30 November 2007
= 59 ÷ 20
= 2 r 19
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 19, this means that on the first day of the remaining 19 days, they would meet in the gym again.
Number of times that they met in the gym in October 2007 and November 2007
= 2 + 1
= 3
Answer(s): (a) 23 Oct 2007; (b) 3
