SOLUTION: Suppose that Hortense and Mort can clean their entire house in 10 ​hours, while their​ toddler, Mimi, just by being​ around, can completely mess it up in only 6 h
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Question 1093176: Suppose that Hortense and Mort can clean their entire house in 10 hours, while their toddler, Mimi, just by being around, can completely mess it up in only 6 hours. If Hortense and Mort clean house while Mimi is at her grandmother's, and then start cleaning up after Mimi the minute she gets home, how long does it take from the time Mimi gets home until the whole place is a shambles? It will take how many hours? Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website! At time 0, when Mimi arrives home, the fraction of the house that is neat is 1 (the whole house). Each hour after Mimi arrives home the fraction of the house that she messes up is 1/6; each hour that meanwhile Hortense and Mort work the fraction of the house that gets cleaned up is 1/10.
So after t hours, the fraction of the house that is clean is
You want to know when that fraction is 0 -- that is, when the whole house is, as you say, a shambles. So
The whole house will be a shambles 15 hours after Mimi arrives home.
I have a couple of questions about this problem...
(1) What happens after the 15 hours? What does a negative fraction mean in this application??? Does the yard get messed up next? and then the neighbors' houses?...
(2) Does Mimi behave when she is at her grandmother's house?
