document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1093176>Question 1093176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that Hortense and Mort can clean their entire house in 10 &#8203;hours, while their&#8203; toddler, Mimi, just by being&#8203; around, can completely mess it up in only 6 hours. If Hortense and Mort clean house while Mimi is at her&#8203; grandmother's, and then start cleaning up after Mimi the minute she gets&#8203; home, how long does it take from the time Mimi gets home until the whole place is a&#8203; shambles? It will take how many hours? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707805 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13206)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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><BR>\n" );
document.write( "So after t hours, the fraction of the house that is clean is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+%281%2F6%29t+%2B+%281%2F10%29t ALIGN=MIDDLE  ALT=\"1+-+%281%2F6%29t+%2B+%281%2F10%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You want to know when that fraction is 0 -- that is, when the whole house is, as you say, a shambles.  So<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830%2F30%29+-+%285%2F30%29t+%2B+%283%2F30%29t+=+0 ALIGN=MIDDLE  ALT=\"%2830%2F30%29+-+%285%2F30%29t+%2B+%283%2F30%29t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830-2t%29%2F30+=+0 ALIGN=MIDDLE  ALT=\"%2830-2t%29%2F30+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30-2t+=+0 ALIGN=MIDDLE  ALT=\"30-2t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+2t ALIGN=MIDDLE  ALT=\"30+=+2t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15+=+t ALIGN=MIDDLE  ALT=\"15+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The whole house will be a shambles 15 hours after Mimi arrives home.<br><BR>\n" );
document.write( "I have a couple of questions about this problem...<BR>\n" );
document.write( "(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?...<BR>\n" );
document.write( "(2) Does Mimi behave when she is at her grandmother's house?<br><BR>\n" );
document.write( "just kidding....<BR>\n" );
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