Zeph jogged in the gym once every 4 days. Jenson jogged in the same gym once every 7 days. They met on 3 November 2005. There are 30 days in November and 31 days in December.
- 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 November and December 2005?
(a)
Multiples of 4: 4, 8, 12, 16, 20, 24, 28
Multiples of 7: 7, 14, 21, 28
LCM of 4 and 7: 28
Zeph and Jenson met every 28 days.
28 days after 3 November 2005 = 31 Nov 2005
The day that they next met in the gym = 31 Nov 2005
(b)
Since Zeph and Jenson first met on 3 November 2005, they did not meet for the first 2 days of November 2005.
Total number of days from 3 November 2005 to 30 December 2005
= 30 + 31 - 2
= 59
Number of sets of 28 days from 3 November to 30 December 2005
= 59 ÷ 28
= 2 r 3
On the first day of each of the 2 sets of 28 days, they would meet in the gym.
Since there is a remainder of 3, this means that on the first day of the remaining 3 days, they would meet in the gym again.
Number of times that they met in the gym in November 2005 and December 2005
= 2 + 1
= 3
Answer(s): (a) 31 Nov 2005; (b) 3
