Howard jogged in the stadium once every 2 days. Carl jogged in the same stadium once every 7 days. They met on 3 March 2010. 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 2010?
(a)
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Multiples of 7: 7, 14
LCM of 2 and 7: 14
Howard and Carl met every 14 days.
14 days after 3 March 2010 = 17 Mar 2010
The day that they next met in the stadium = 17 Mar 2010
(b)
Since Howard and Carl first met on 3 March 2010, they did not meet for the first 2 days of March 2010.
Total number of days from 3 March 2010 to 30 April 2010
= 31 + 30 - 2
= 59
Number of sets of 14 days from 3 March to 30 April 2010
= 59 ÷ 14
= 4 r 3
On the first day of each of the 4 sets of 14 days, they would meet in the stadium.
Since there is a remainder of 3, this means that on the first day of the remaining 3 days, they would meet in the stadium again.
Number of times that they met in the stadium in March 2010 and April 2010
= 4 + 1
= 5
Answer(s): (a) 17 Mar 2010; (b) 5
