document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=398287>Question 398287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Anne and Robert decide to meet between 6 and 7 pm for dinner but agree that each should wait no longer than 10 minutes for the other.  Find the probability that they meet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282279 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=282279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = # minutes after 6 pm when Anne came, and<BR>\n" );
document.write( "y  = # minutes after 6 pm when Robert came.  <BR>\n" );
document.write( "Then the sample space S = {(x,y): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C+x ALIGN=MIDDLE  ALT=\"0+%3C+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C+60 ALIGN=MIDDLE  ALT=\"y+%3C+60\"   DISABLED_style= \"max-width:90%; height:auto;\" >} is the (open) square with vertices (0,0), (0,60), (60,0), and (60,60).<BR>\n" );
document.write( "What is wanted is the intersection of the sample space S with the region satisfying<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28y-x%29+%3C+10 ALIGN=MIDDLE  ALT=\"abs%28y-x%29+%3C+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or equivalently,\r<BR>\n" );
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document.write( "-10 < y-x < 10.\r<BR>\n" );
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document.write( "The boundaries of this double inequality are the lines y - x = -10 and y - x = 10.<BR>\n" );
document.write( "All points between these two lines (excluding the lines themselves) satisfy the preceding double inequality.  Call this region R.\r<BR>\n" );
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document.write( "Then what is desired is the area of S intersection R. This area is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BS%5D+-+A%5BS-R%5D ALIGN=MIDDLE  ALT=\"A%5BS%5D+-+A%5BS-R%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BS%5D ALIGN=MIDDLE  ALT=\"A%5BS%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = area of sample space S, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BS-R%5D ALIGN=MIDDLE  ALT=\"A%5BS-R%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the area of S-R.\r<BR>\n" );
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document.write( "Then the probability is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%5BS%5D+-+A%5BS-R%5D%29%2FA%5BS%5D ALIGN=MIDDLE  ALT=\"%28A%5BS%5D+-+A%5BS-R%5D%29%2FA%5BS%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Incidentally, S-R consists of two congruent triangles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5B1%5D ALIGN=MIDDLE  ALT=\"T%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5B2%5D ALIGN=MIDDLE  ALT=\"T%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5B1%5D ALIGN=MIDDLE  ALT=\"T%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > has vertices (0,10), (50,0), (50,60)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5B2%5D ALIGN=MIDDLE  ALT=\"T%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > has vertices (10,0), (60,0), (60,50)<BR>\n" );
document.write( "(Each triangle has area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A50%5E2 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A50%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
document.write( "The probability that Anne and Robert meet is then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2860%5E2+-+2%2A%281%2F2%29%2A50%5E2%29%2F60%5E2+=+%2860%5E2+-+50%5E2%29%2F60%5E2+=+11%2F36 ALIGN=MIDDLE  ALT=\"%2860%5E2+-+2%2A%281%2F2%29%2A50%5E2%29%2F60%5E2+=+%2860%5E2+-+50%5E2%29%2F60%5E2+=+11%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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