document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=954056>Question 954056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Person in A(8,0) and B(8,10) hear the sound of explosion right at the same time. While another person in C(-8,0) just heard the sound 12 seconds later. If the distance is in km and sound travels at 1/3 km/s, what is the coordinate of the explosion? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #582680 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=582680\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if point C heard the explosion 12 seconds after it occurred, and sound travels at 1/3 kilometer per second, then the explosion must have been 4 kilometers away from point C.\r<BR>\n" );
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document.write( "If both points A and B heard it as the same time, then the explosion must have been exactly halfway between points A and B.\r<BR>\n" );
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document.write( "That puts the explosion on the circumference of a circle around point C and the perpendicular bisector of the line between points A and B.\r<BR>\n" );
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document.write( "Both conditions will be satisfied at the intersection of the circle with the line.\r<BR>\n" );
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document.write( "the perpendicular bisector of the line between points A and B is the line y = 5.\r<BR>\n" );
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document.write( "the location of the circle around point C depends on the scale of the graph.\r<BR>\n" );
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document.write( "the solution will be the intersection between the perpendicular bisector of the line between point A and B, and the circle surrounding the point C.\r<BR>\n" );
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document.write( "If the scale on the graph is one unit per kilometer, there will be no intersection and your problem will not have a solution.\r<BR>\n" );
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document.write( "The circle around point C is 4 km away from point C.\r<BR>\n" );
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document.write( "At 1 km per unit, that means the circle is 4 units away from point C on the graph.\r<BR>\n" );
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document.write( "As such, it will not intersect with the line y = 5 because the highest it will go is the point (-8,4).\r<BR>\n" );
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document.write( "here's a graph of that occurrence.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/030901.jpg\" alt = \"$$$\" </>\r<BR>\n" );
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document.write( "If the scale on the graph is 4/5 of a unit per kilometer, there will be one intersection and your problem will have exactly one solution.\r<BR>\n" );
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document.write( "The circle around point C is 4 km away from point C.\r<BR>\n" );
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document.write( "At 4/5 km per unit, that means the circle is 5 units away from point C.\r<BR>\n" );
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document.write( "As such, it will intersect with the line y = 5 at the point (-8,5).\r<BR>\n" );
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document.write( "At that point, point C heard it 12 seconds after it occurred and points A and B heard it at the same time.\r<BR>\n" );
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document.write( "here's a graph of that occurrence.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/030902.jpg\" alt = \"$$$\" </>\r<BR>\n" );
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document.write( "If the scale on the graph is 1/2 of a unit per kilometer, there will be two intersections and your problem will have exactly two solutions.\r<BR>\n" );
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document.write( "The circle around point C is 4 km away from point C.\r<BR>\n" );
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document.write( "At 1/2 km per unit, that means the circle is 8 units away from point C.\r<BR>\n" );
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document.write( "As such, it will intersect with the line y = 5 at the points (-14.24,5) and (-1.76,5).\r<BR>\n" );
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document.write( "At those points, point C heard it 12 seconds after it occurred and points A and B heard it as the same time.\r<BR>\n" );
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document.write( "here's a graph of that occurrence.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/030903.jpg\" alt = \"$$$\" </>\r<BR>\n" );
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document.write( "If the scale on the graph is 1/3 of a unit per kilometer, there will be two intersections and your problem will have exactly two solutions.\r<BR>\n" );
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document.write( "The circle around point C is 4 km away from point C.\r<BR>\n" );
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document.write( "At 1/3 km per unit, that means the circle is 12 units away from point C.\r<BR>\n" );
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document.write( "As such, it will intersect with the line y = 5 at the points (-18.91,5) and (2.91,5).\r<BR>\n" );
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document.write( "At those points, point C heard it 12 seconds after it occurred and points A and B heard it as the same time.\r<BR>\n" );
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document.write( "here's a graph of that occurrence.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/030904.jpg\" alt = \"$$$\" </>\r<BR>\n" );
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document.write( "Bottom line is the graphical solution depends heavily on what the scale of the map is.\r<BR>\n" );
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document.write( "That information is missing.\r<BR>\n" );
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document.write( "If, in fact, you did not mean that point C heard it 12 seconds after the explosion, but you meant that point C heard it 12 seconds after points A and B heard it, then you have a different situation and a different solution.\r<BR>\n" );
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