SOLUTION: I would really appreciate your help solving this problem. I have tried many different times and really do not know how to go about solving it. My attempts to solve are shown belo

Question 121767: I would really appreciate your help solving this problem. I have tried many different times and really do not know how to go about solving it. My attempts to solve are shown below the problem. Thank you.
Sue and Treg just started dating on Jan 1, 2008. Treg has every 9th day off startiing on Sunday. Sue has every 6th day off starting on monday. Sue's dad says that they can borrow his new car to go on a date into Chicago the next time that she and Treg both have the same day off. After a month, Sue is convinced that they will NEVER have the same day off. Treg doesn't believe that this can be the case. With whom do you agree?
I believe that they will have a day off because 6 & 9 are the same multiplier, they are each multiples of 3. I just do not know how to make the formula to answer the question. I tried this formula and it didn't work.
1/9 + 1/6 = 1/x
x18=x18
18/9+18/6 = 18/x
2+3=18/x
5=18/x
5x=18
x=3.6
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I think the problem here is T's cycle, of 9 days off, starts on Sunday; and S's cycle of 6 days off started on Monday, so no matter what multiple of both comes up 18, 36, 54 etc, it is always off-set by one day. S is right I don't think it would ever happen.
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