Question

father has 3 sons, one of them isits him every 3 days, the second every 5 days and the third every 6 days. How many times are they going to meet after 60 days?

Answer 1

The sons will meet their father together twice after 60 days. For individual visits, the first son will visit 20 times, the second son 12 times, and the third son 10 times, totaling to 42 visits in 60 days.

Step-by-step explanation:

To solve the problem of how many times the sons will meet their father after 60 days, given that one visits every 3 days, another every 5 days, and the third every 6 days, we need to find the least common multiple (LCM) of the numbers 3, 5, and 6. The LCM of 3, 5, and 6 is 30, which means that all three sons will visit their father together every 30 days. Since there are 60 days in the time frame given, they will all meet together twice.

If the question is asking about individual visits without the need for all three brothers to be together, we would count the number of visits for each one within the 60 days: for the first son, it would be 60 divided by 3, resulting in 20 visits; for the second son, it would be 60 divided by 5, resulting in 12 visits; and for the third son, it would be 60 divided by 6, resulting in 10 visits. The total number of individual visits would therefore be 20 + 12 + 10 = 42 visits.

Answer 2

The sons visit their father on the same day every 30 days. Within a 60-day period, they will all meet twice.

Step-by-step explanation:

The problem presented is asking to determine the frequency at which three sons visit their father and to calculate how many times those visits coincide within a 60-day period. This is a problem of finding the least common multiple (LCM). The first son visits every 3 days, the second son every 5 days, and the third son every 6 days. To find out how often all three sons will visit their father on the same day, we calculate the LCM of 3, 5, and 6.

• The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60...
• The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60...
• The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60...

By looking at these multiples, we can see that the least common multiple is 30. Therefore, all three sons will meet with their father every 30 days. Within a 60-day period, this will happen twice. So, the sons will meet with their father on the same day a total of 2 times within 60 days.