Ooh logic puzzle.
Let me try to figure this out in my head.
There are two answers!
The theoretical answer:
Ok so yes when the minute is over the manager is done checking rooms.
If you have to divide by 2 each time you check a room, doing at half the speed of the other than you would evenutally get to an incredibly small amount of time, an infinite one. It is possible to get an infinite task done in a less than infinite amount of time because all units of time are infinite. If keep dividing the time needed by 2 you will eventually get to the point where the problem you are doing is (∞/∞). Due to all laws of mathematics this is equal to the number 1. Some people say that if divide infinity by infinity you just get infinity. That is incorrect. First of all infinity is not a number so you canto divide it VIA THE LAWS OF MATH, you can however divide it using logic. To divide using logic, use your logic. Logic is what math is made up of. Math is a form of logic, and logic a form of math. So by using logic we go around the mathematical paradox of infinity and say that (∞/∞ = 1). This means in terms of Time the manager has 1, In terms of Rooms the manager has 1. If we do Work over Time (W/T). If the Work is equal to or less the Time than you can complete the Work in the set Time. In the Example above Time = 1, and Work = 1, so (W/T = 1/1) Meaning the manager would have enough time to complete checking all the rooms.
The Physical answer:
The physical answer is much much simpler than the one above. The physical answer is still yes but includes the laws of physics. Simply the less time there is the more time there is. I know that sounds insane but if the manager went slowly to an infinite place in time, we would quickly reach the spot where she is at or gone above the speed of light, therefore allowing her to continue to do her job while time is frozen. No the physical world would not be frozen in place. She would have an infinite amount of time to do her infinite job. At some point she would go so fast that the best conclusion to draw is that she would start reversing time itself. It is theoretically possible if you have enough mass from going above light speed. Because the time she is reversing is already frozen from before she would not travel back in time but reverse it while still getting all the infinite Work done. She would finish before she started which would put the equation at, (W/T = 1/0 = 1/1) therefor completing her task.
Thx for the logic puzzle.