A milkman and a baker deliver to the same house.
In a period of 28 days, the milkman calls every second day and the baker every third day.
They meet at a house twice in 7 days
How many more times do they meet during the four week period?
They will meet 3 times after the first week. They will meet on the 13th, 19th and 27th.
Milkman 2 4 6 8 10 12 14 16 18 20 22 24 26 28
Baker 3 6 9 13 15 18 21 24 27
What is your answer?
2, right?
I just caught a mistake. The baker went to the house on the 12th, not the 13th.
Yes, 2 more times.
it should be 3 because they say they meet on the first week so they both meet on the 12th,18th and 24th.
To solve this problem, we can use the concept of the least common multiple (LCM) of two numbers. In this case, we need to find the LCM of 2 and 3, which is the smallest number that is evenly divisible by both 2 and 3, without leaving a remainder.
The LCM of 2 (milkman's interval) and 3 (baker's interval) is 6, meaning that every 6 days, they will meet at the house.
We can divide the 28-day period into 4 groups of 7 days each. In each group, the milkman calls every second day, and the baker calls every third day.
In the first 7 days, the milkman calls on days 2, 4, 6, and the baker calls on days 3 and 6. Thus, they meet once on the 6th day.
In the second 7 days, the milkman calls on days 8, 10, 12, and the baker calls on days 9 and 12. Thus, they meet once on the 12th day.
In the third 7 days, the milkman calls on days 14, 16, 18, and the baker calls on days 15 and 18. Thus, they meet once on the 18th day.
In the fourth 7 days, the milkman calls on days 20, 22, 24, and the baker calls on days 21 and 24. Thus, they meet once again on the 24th day.
Therefore, within the 28-day period, the milkman and the baker meet 4 times in total.
To calculate the number of times they meet during the four-week period, we subtract the initial two meetings:
Total meetings = 4 - 2 = 2
So, they meet 2 more times during the four-week period.