My friend and I are both going to start working. I'm starting Sunday and will have every 9th day off. She's starting Monday (the day after me) and will have every 6th day off. When is the first day we'll both have off to go to the mall? I'll need the formula along with the name of the day. Thanks.
Sun MTWTFS Sun MTWTFSat SunMTWTHS
Her days off, 2Mon, 3Wed, 4Fri, 5Sun...
Your days off, 1Sat, 2Fri, 3Thur, 4Wed,
so, extend this out to get a common day.
the numbers is the week
9Wed is the ninth week, wednesday, for instance.
To find out when you and your friend will both have a day off to go to the mall, you can use the concept of finding the least common multiple (LCM) of the two given intervals. In this case, your day off occurs every 9 days, and your friend's day off occurs every 6 days.
To find the LCM, you can use the following formula:
LCM(a, b) = (a * b) / GCD(a, b)
Where a and b are the two numbers or intervals you want to find the LCM for, and GCD(a, b) represents the greatest common divisor between those numbers.
In this case, a = 9 and b = 6. The GCD(9, 6) is 3 since 3 is the largest number that divides both 9 and 6 evenly.
Now, substitute these values into the formula:
LCM(9, 6) = (9 * 6) / GCD(9, 6)
= (54) / 3
= 18
Therefore, the LCM of 9 and 6 is 18. This means that after every 18 days, both you and your friend will have a day off together.
To determine the day of the week for this day off, you can count the days from the starting day (Sunday for you) until the 18th day. Since you already know that you start on Sunday, you can count the days of the week by adding multiples of 7.
Starting from Sunday, add 18 days:
Sunday -> Monday -> Tuesday -> Wednesday -> Thursday -> Friday -> Saturday -> Sunday -> Monday
After 18 days, your first common day off will be on a Monday.
Therefore, the first day you and your friend will both have off to go to the mall is the Monday that occurs after 18 days from when you start working.