Question 1093176
<br>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.<br>
So after t hours, the fraction of the house that is clean is
{{{1 - (1/6)t + (1/10)t}}}<br>
You want to know when that fraction is 0 -- that is, when the whole house is, as you say, a shambles.  So
{{{1 - (1/6)t + (1/10)t = 0}}}
{{{(30/30) - (5/30)t + (3/30)t = 0}}}
{{{(30-2t)/30 = 0}}}
{{{30-2t = 0}}}
{{{30 = 2t}}}
{{{15 = t}}}<br>
The whole house will be a shambles 15 hours after Mimi arrives home.<br>
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?<br>
just kidding....