This is not math homework. I am 36 years old and dumb and trying to literally puzzle out watering schedules. I am sorry for the horrific brain puke below.
A and B share plant watering duties based on their schedules.
A has a 14 day rotation of guaranteed watering days, regardless of B’s schedule.
A always waters on days 4, 9, 13, and 14
B’s watering schedule is based on his work schedule, which is two days on, four days off.
On days when B works, A always waters the plants. But when B is off, B waters the plants only if it is also not A’s watering day
Because A is on a 14 day rotation, and B is on a 6 day rotation, I figured that after 42 days (that being the LCM of the two) we would have a full cycle, is that correct?
If so, when I “calculated” who actually waters more I got
A: 22
B: 20
I literally mapped out their two schedules in excel of 42 rows, first I filled in A’s guaranteed days and then B’s work schedule, while making sure that those were A’s as well
Did I do something wrong, or is this number correct (and 42 is enough days)
If so does anyone know what the formula might have been to calculate it instead of plotting it, or how I can calculate the ratio that the two approach as more and more weeks pass?
I’ve rarely seen a more equitable distribution of watering responsibilities. It’s usually more like 5/37, and the one who’s picking up the slack for the other one suffers, or, worse, 5/22, and the plants are the ones who end up suffering.
Failing any of that, automated drip irrigation is the bomb.
Your method is sound. But if you wanted to do it more succinctly: B is off 2/3 of the time. On a day when B is off, there is a 10/14 chance that it will not be A’s watering day. So B will water 210 days out of 143, or 20/42, just like you found.
Now, it could be a bit more complicated than that. The two schedules have a common factor, so it would be possible for the schedules to synch up, such that when A was off, it’d be more likely that B would be, too (or the reverse). But that’s not an issue, because the only common factor is 2, and so as long as at least one of them has as many even days off as odd (both do, in fact), this synching won’t happen.
And what kind of plants are these, that need watering every day? Most plants can go a couple of weeks between waterings.
Not so fast. Suppose that B’s schedule is two days on, four days off as before, BUT he works On-Off-On-Off-Off-Off. Suppose A always waters on days 2, 6, 10, 14. I think you’ll find that A ends up watering 26 days out of 42, and B only 16. Conversely, if A’s days were 1, 6, 11, 13, it is B that ends up watering more days than A.
No, I don’t have a general formula for counting scheduled watering days.
Thanks for the confirmation of my math Chronos and for feedback.
Now for 100% honesty this schedule was not about watering plants but who has the kids (as some of you probably suspected), thanks for helping the side of justice (and the kids).
Suppose that B’s schedule is two days on, four days off as before, BUT he works On-Off-On-Off-Off-Off. Suppose A always waters on days 2, 6, 10, 14. I think you’ll find that A ends up watering 26 days out of 42, and B only 16. Conversely, if A’s days were 1, 6, 11, 13, it is B that ends up watering more days than A.