Tom jogged in the stadium once every 3 days. Charlie jogged in the same stadium once every 4 days. They met on 7 May 2015. There are 31 days in May and 30 days in June.
- On which date they next met each other in the stadium? Give your answer in the following format. (Eg 1 Jan 2000)
- How many times did they meet in the stadium in May and June 2015?
(a)
Multiples of 3: 3, 6, 9, 12
Multiples of 4: 4, 8, 12
LCM of 3 and 4: 12
Tom and Charlie met every 12 days.
12 days after 7 May 2015 = 19 May 2015
The day that they next met in the stadium = 19 May 2015
(b)
Since Tom and Charlie first met on 7 May 2015, they did not meet for the first 6 days of May 2015.
Total number of days from 7 May 2015 to 30 June 2015
= 31 + 30 - 6
= 55
Number of sets of 12 days from 7 May to 30 June 2015
= 55 ÷ 12
= 4 r 7
On the first day of each of the 4 sets of 12 days, they would meet in the stadium.
Since there is a remainder of 7, this means that on the first day of the remaining 7 days, they would meet in the stadium again.
Number of times that they met in the stadium in May 2015 and June 2015
= 4 + 1
= 5
Answer(s): (a) 19 May 2015; (b) 5
