Gabriel jogged in the stadium once every 4 days. Jenson jogged in the same stadium once every 5 days. They met on 9 March 2011. There are 31 days in March and 30 days in April.
- 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 March and April 2011?
(a)
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 5: 5, 10, 15, 20
LCM of 4 and 5: 20
Gabriel and Jenson met every 20 days.
20 days after 9 March 2011 = 29 Mar 2011
The day that they next met in the stadium = 29 Mar 2011
(b)
Since Gabriel and Jenson first met on 9 March 2011, they did not meet for the first 8 days of March 2011.
Total number of days from 9 March 2011 to 30 April 2011
= 31 + 30 - 8
= 53
Number of sets of 20 days from 9 March to 30 April 2011
= 53 ÷ 20
= 2 r 13
On the first day of each of the 2 sets of 20 days, they would meet in the stadium.
Since there is a remainder of 13, this means that on the first day of the remaining 13 days, they would meet in the stadium again.
Number of times that they met in the stadium in March 2011 and April 2011
= 2 + 1
= 3
Answer(s): (a) 29 Mar 2011; (b) 3
