document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043954>Question 1043954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,distance and time are not really my strong points...<BR>\n" );
document.write( "Winnie and Piglet decided to visit one another and set off at the same time to each others house. When they met on the road joining their houses, they forgot that they wanted to see each other and continued walking. Winnie reached Piglet's house 8 minutes after the meeting and Piglet got to Winnie's house 18 minutes after the meeting. How long did it take Piglet to reach Pooh's house from the time he left his own house? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659177 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w\"> represent the speed with which Winnie walked and let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> represent the speed with which Piglet walked.  The entire distance from Winnie's house to Piglet's house is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\"> and we can divide that distance into two pieces, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d_1\">, the distance from Winnie's house to the point where they met, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d_2\">, the distance from Piglet's house to the same point.  And we know that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d_1\ +\ d_2\ =\ d\">. Since we know they left at the same time, the time it took each of them to get to the meeting point is the same amount of time and we will call that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">.\r<BR>\n" );
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document.write( "Since we know that distance equals rate times time, we can now establish some relationships between the above variables.\r<BR>\n" );
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document.write( "The distance from Piglet's house to the meeting point can be expressed in two different ways:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d_2\ =\ pt\">\r<BR>\n" );
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document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is Piglet's rate and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> is the time it took Piglet to get to the meeting point, and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d_2\ =\ 8w\">\r<BR>\n" );
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document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w\"> is Winnie's rate and it took Winnie 8 minutes to get to Piglet's house after the meeting point.  But then we can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{8w}{p}\">\r<BR>\n" );
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document.write( "Similarly, considering the distance from Winnie's house to the meeting, we can come up with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{18p}{w}\">\r<BR>\n" );
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document.write( "And now we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{8w}{p}\ =\ \frac{18p}{w}\">\r<BR>\n" );
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document.write( "A little algebra gets us to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ w^2\ =\ \frac{9}{4}p^2\">\r<BR>\n" );
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document.write( "Which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ w\ =\ \frac{3}{2}p\">\r<BR>\n" );
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document.write( "And now we know that Winnie walked one and one-half times as fast as Piglet.\r<BR>\n" );
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document.write( "Going back to an earlier relationship we had established:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d_2\ =\ 8w\">\r<BR>\n" );
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document.write( "Now substitute <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{3}{2}p\"> for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d_2\ =\ 8\left(\frac{3}{2}p\right)\ =\ 12p\">\r<BR>\n" );
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document.write( "Now we know it took Piglet 12 minutes to get to the meeting place and 18 minutes to get from the meeting place to Winnie's house for a total of 30 minutes.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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