Cody jogged in the gym once every 4 days. Ethan jogged in the same gym once every 6 days. They met on 3 April 2007. 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 2007?
(a)
Multiples of 4: 4, 8, 12
Multiples of 6: 6, 12
LCM of 4 and 6: 12
Cody and Ethan met every 12 days.
12 days after 3 April 2007 = 15 Apr 2007
The day that they next met in the gym = 15 Apr 2007
(b)
Since Cody and Ethan first met on 3 April 2007, they did not meet for the first 2 days of April 2007.
Total number of days from 3 April 2007 to 30 May 2007
= 30 + 31 - 2
= 59
Number of sets of 12 days from 3 April to 30 May 2007
= 59 ÷ 12
= 4 r 11
On the first day of each of the 4 sets of 12 days, they would meet in the gym.
Since there is a remainder of 11, this means that on the first day of the remaining 11 days, they would meet in the gym again.
Number of times that they met in the gym in April 2007 and May 2007
= 4 + 1
= 5
Answer(s): (a) 15 Apr 2007; (b) 5
